My good deed for the day...

Yes, there are possible compatibility issues.

Handlebars are offered in several different diameters where the stem clamps to them. You will need to check the diameter with a caliper. If it is 31.8 mm you are halfway there. There is a real chance that it will measure 25.4 mm, as that is the other "standard" diameter. If it does, you cannot use the stem to which you have linked. (There is a smaller chance that it will measure something completely different. This also destroys your dream.)

The steerer tube (the part that sticks up out of the frame, to which the stem attaches) also comes in different diameters. If it measures 1 1/8" inch, you are good to go. And yes, they did make one end of the stem metric and the other end Imperial just to screw with you. And yes, there is a real chance that it will measure one inch, or even 25mm, or 26mm, or 1 1/4", all of which also ruin your dream.

For further information, here's Sheldon. If you have any sense at all, this will make you give up bicycles entirely.

HTH!