Is it neccesary to pull-up the reset pin on home made Arduino board?

The other problem is that by default the pull up resistors are not enabled. Therefore you can't use it until the code is running. The code can't run unless this pin is high. See the problem?

I have a few battery powered gadgets that don't have an external pull-up and they have been very reliable.

What you mean is that you have not detected any problems with the limited use you have given this project. The rule in electronics is that if the data sheet says something is needed you better be pretty dam sure of what is happening if you ignore it. Otherwise all bets are off and the manufacturers will not be held responsible for anything the chip consequently does or does not do. For god sake it is only a resistor, even on my penny pinching projects that were made in there millions we would not do such a stupid thing.