Hi Athaela,
It doesn't take long at all. I'd say maybe under 5 minutes. As for if it will actually repair the game or not, that really depends on what's really wrong with the game.
Repair Game checks all of the game's files on your computer against the files on Origin's servers. It then downloads and replaces any files that don't match. It (as far as I know) doesn't affect any files in your Documents\Electronic Arts\The Sims 3 folder, but it's a good idea to back that up before running Repair Game.
Hope this helps, and Welcome to the forum!!
MrsFlynn