I've found a very old NXTasy thread that answers this question definitively.
Flemming Bundgaard, from LEGO, ran two or three test-to-failure runs with my NXTTools utility repeatedly setting the brick into firmware download mode and downloading the standard NXT firmware to the brick. In each of his tests the brick failed, if I recall correctly, after ~...
I’ve had a quick look through the MindSqualls code and it looks like you can. I cannot test this however as I don’t have two kits.
Note: I believe it is preferred to NxtBrick class rather than McNxtBrick class as the latter is for a special program used for precise control over the NXT motors.
LEGO Mindstorms all use flash storage which does have a limited number of write cycles, so the answer is technically yes in some capacity, but it's probably not something you need to worry about.
A LEGO Mindstorms NXT 2.0 uses a Atmel AT91SAM7S256 microcontroller. This board has 256 KB flash memory, which is roughly the size of the latest firmware image.