I have a project that uses a 7.2V battery pack for power. Up to this point, every time I need to recharge the pack I remove the power plug from my Arduino and plug in the charger to it. Works well of course, but I need to wait until the pack is charged to continue to work.
That pack power is also connected as DC motor power.
My question is: if I install two plugs in parallel on the wire that comes from the battery pack, connect one to the Arduino and the other to the charger every time the pack needs to be charged, will this setup charge the batteries and at the same time keep power to the circuit at around 7.2 to 7.5V?
Looks very much like a "constant current" charger which means it will adjust the output voltage to keep the current flowing. If you have it charging the battery and feeding the arduino, then, if the battery becomes disconnected, the charger will increase its output voltage in an endeavour to keep the current flowing. As it's rated to charge 12 volt battery systems this implies it will be capable of increasing the output voltage above 12 volts, which may endanger your arduino.
I also wouldn't recommend to do it. Charger has intelligence capability
Automatic matching of charging current is a feature of this quality Charger.
so if the load isn't only battery, it would mix up charging process. And one more things, trigger "fully charged" for NIMH battery usually based on delta V method, which also would be affected if arduino connected in parallel.