flubbersaurus:
yes, the arduino will run your program when powered by battery,
although, like when you boot up a p.c,
and it takes a few minutes,
the arduino will take about a 2 second delay.
hope this helped
I guess you didn't read or understand the prior reply?
If you install optiboot (bootloader, as used in the standard Uno board) it doesn't wait on power-on, only on reset.