Exactly!
The only concern I'd have would depend on how you've installed any mods you're using. If you used JSGME the whole time, you should be mostly safe. I tried an uninstall from that before though and it ended up leaving some folders behind and I had really odd "errors". Actually turned out some of the errors was NYGM actually acting properly, (when before it hadn't!) but I digress.
I'd still contact Ubisoft and get a pristine install image again, or just go out and buy the game locally or online. It's $19.82 at
Wal Mart, and $18 something at
Amazon and Office Depot of all places. Some online retailers at Amazon even have it as low as $9.75!