Correct me if I'm wrong,
Assuming you're running a relativly stock arduino without sd card reader or other storage,
when you upload the next sketch/program into the arduino the previous one gets erased from the arduino.
The memory it is stored in is non volitile (does not wipe as soon as power is lost) memory..
True but that's not what the OP's asking. His concern is that if he builds circuit B and powers up, the old sketch for circuit A will run before he loads the new sketch for circuit B, and that could have consequences.