Timer circuit power usage in off state

Many of my Arduino projects are battery powered and I normally use a latching relay (controlled by the arduino) to power down then completely between interactions. In this case I wanted a 'separate ca 2-5 minute timer' circuit. I know very little about this so I googled and found this:

Is this circuit going to draw any power in 'off state'? since I want it to function over long period of times even small currents in off state is not possible..

If I wanted to replace the second transistor (and relay) with something capable of handling more current, would that be possible and do you have a suggestion on what transistor to use? I need it to handle max 5V/0,4A.