Will I cause any damage if I place the transfer case in neutral and drive it, I noticed it will move with the transfer case to neutral and I moved it 2-3 feet in drive and reverse? Thanks in advance.

 

Without knowing what it is you are driving its really hard to say.
But I assume you are driving a Land Rover, and because all modern Land Rovers are full time four wheel drive you cannot drive it with the transfer case in neutral, it will not move.
If your's moved it is because it was not completely in neutral.
If you were to leave the transfer case in neutral and the transmission in park it would roll away if parked on a hill.