I'm considering this design to allow the Arduino to power off the device, but I'm curious if this circuit will slowly drain the battery while waiting to be turned on?
Jump to the inaccurately named final post for an updated schematic and code
If as long as that doesn't mean leakage current of that MOSFET itself, there are no causes leakage issues at your circuits.
No, to be more specific. After the Arduino lowers pin 7 and turns the circuit off, will the circuit continue to draw any power from the battery while it is off?
Here is my take on zero power off switches
Long Life On/Off Remote
"with the FET switch OFF, i.e. ~10nA leakage"
I intended to answer about it.
I don't think there is a problem with the your circuits.
However, the off state MOSFET still has a very small leakage current.
Ignore it because it is less than the self-discharge of the battery.
That's I wanted to say.
You might sleep better at night if you just built it and used something like an ammeter to see for yourself.
a7
Thank you. I've marked this as the solution.
I appreciate everyone's time.
I'm building it tomorrow after Amazon delivers the fets I just ordered. I love next day delivery.
I was just curious if I needed to put a hard switch between this and the battery.
I'm using a 7.4V high discharge LiPo. This circuit will make and close a relay for the higher draw devices like motors, servos, sensors, LED strip.
So this circuit will only power the Arduino, itself, and a relay coil.
If you hadn’t thought to, you could use the Arduino to keep an eye on the battery voltage. If you are taking about the kind I think, they def do not like to be discharged below a certain voltage.
Also I like the relay, as it means you can totally disconnect the battery from your power circuits, but I do know there are battery systems that switch on and almost totally off everything with mosfets.
But if you are using a relay, you could arrange a circuit where the relay supplied power to the Arduino as well as to your high power circuits.
The pushbutton would jump start things, the relay would hold power going until the Arduino shut the relay off, shutting off voltages for everyone, total unconnected lipo.
I use 2s and 3s lips and when 5 volts is needed employ a buck regulator. This could be downstream to the relay and supply the microprocessor.
a7
Before landing on this circuit I made an SR-latch with two relays to achieve the same end, but this fet way only uses one relay controlled by the Arduino. That way I can shut off the high draw stuff from within the program.
Is your described method similar in functionality? I'm interested to learn different approaches.
I didn't think to monitor the voltage. I thought these delivered constant voltage until cut off. Have I misread something possibly?
I suppose a 10:1 voltage divider and any analog pin would do the job.
The voltage of 3.7V per cell is for convenience value, one fully charged cell can rise to 4.2V.
And don't discharge it to less than 3.2V per cells.
So in the case of a 2 cells battery pack, it is used within the voltage range of 6.4V to 8.4V.
Charging above 8.4V or discharging below 6.4V will seriously damage and destroy the battery.
In some cases, it makes smoke and flames.
That defeat your house and probably you...
So monitor the voltage, got it.
Sounds like good advise.
Yes, no… that kind of battery has nothing but the bare cells in series. It is incumbent upon the user to cease drawing current when the voltage gets too low.
I stop when under load (heavy load) the voltage goes below about 3.3 volts per cell, and I look to have a recovery voltage of 3.7 volts.
This leaves a lot of power unused, but yields very good battery life.
Similarly, I charge to 4.17 volts, every 0.1 below the nominal 4.2 permissible again is good for the cell, at the expense of operating time - so I live with that or use a larger battery than I would if I was willing to keep buying new ones, and take risks at the low end that I am not interested in. Taking.
Now I drew you a latching relay circuit but can't get it into this post at this time, but it is simple, just a pushbutton in parallel with the relay contacts that supply all power. As soon as you push the button, the Arduino take over by energizing the relay, and continues to do until it's time to shut down, when it just releases the relay and everything is dead.
An analog input and as you say appropriate voltage divider is a perfect way to keep an eye on the battery. Obsessive types might even go so far as to monitor every cell; with good batteries well cared for and always balance charged, it should not be necessary… my batteries end up balanced after use, when they don't I know it is the beginnings of the end for a cell and therefor the battery. I do not do repairs on lipos.
See battery university dot com or something like that, it has more than you could ever want to know about all kindsa batts.
One last must know fact: if you aren't going to use a lipo, discharge or charge it as you must to achieve 3.7 volts per cell, some say 3.8, but the point is neither charged nor depleted. Leaving a lipo charged for a day is about like putting a full cycle on it I have seen said, dunno for sure but it is a good idea even if a PITA to charge, then use, then balance charge to the storage voltage.
a7
It isn't necessary to monitor the voltage of each cell during use if it is balance charged every time it is re-charged.
It is enough to monitor the overall voltage.
The balance is hardly lost by one discharge.
However, unless the battery is out of order.
Again, my thanks. That does simplify things.
The charger LEDs go from red to green when each cell is charged. If the battery is out of order will one of these LEDs always indicate an out of order battery or do I need a better approach to check the battery health?
The charger manual only mentions the LED colors, nothing about diagnostics.
This is my first time with Li-Po batteries.
I'm sorry to but I'm not familiar with the specifications of that a simple charger. 
Because I'm using a computer controlled integrated Li-po manager that can does charge / discharge / rebalance / health check.
It can freely select charge / discharge current, finaly charge / discharge voltage(a.k.a number of cells), over temprature sensing.
In health check, voltage and current draw capacity is measured at each cell.
I'm pretty cautious about using Li-po because I'm afraid of blaze it... 
I will have the Arduino log the battery charge level when it is changed out each time. I imagine I will see it slowly decline until I hit 150 charges or so. I could have a greater change trigger a battery replacement warning for the system.
That's probably the best I'm going to get as far as battery health goes.
As @alto777 says, it's safer to use with a more safety margin.
The effective capacity of the battery will be lower than the rating, but the risk reduction is very important.
Because the li-po battery is a considerable dangerous component.
Those used in mobile phones contain multiple protection circuits that are quite redundant...
