Can I fit a 32-622 tire on a 32-630 rim? Can I fit a 32-622 tire on a 32-630 rim?
The tire diameter is 8 mm smaller than the rim, so it's going to be tight - but will it fit with some extra force, and might there be any other problems?
No.

You would need to stretch the tire circumference by 25 mm for it to fit. If the tire has steel beads (cables at the edges) stretching them is theoretically if not practically possible but the rest of the tire structure is fabric that does not stretch.