Using the mv command to move files from one volume to a different volume is a copy operation. But how would you run out of space on the source volume? You would only run out of space on the target volume if that volume is smaller than the total size of the files you're moving. But either way, you're only deallocating space on the source volume, not allocating more space on it.
If you use mv to "move" files from one directory to another on the same volume, that's just a rename operation. You're not copying data, you're just adjusting file pointers to present a different directory hierarchy. You're not going to run out of space because the file data stays right where it was.
Either way, I'm not sure I see the problem. :-) Have you actually been trying this and running out of space, or are you just trying to plan ahead?