It probably won't even load and even if it did it would be wrong. You need to calibrate each PC and each monitor combination.
Assuming that it is a standard profile (e.g., .ICC or .ICM) it will certainly load, and will be approximately correct, assuming that your color management environment is ok. Although its better to calibrate each display board and monitor combination separately, the variance in display board calibration is far, far less than the variation between monitors.
Note that this does assume that you have a clean color management environment on both systems - no LUT management software or anything like that. If you have different, non-standard software on each machine, all bets are off.