I'm kind of worried after reading through what Overwatch does, will it get screwy if you have aging turned off with the in-game option..?

Hi there. The best place to post is really Chatterbox, that's the general discussion forum. These internal boards don't get much in the way of traffic except by management and some very dedicated members (or those who get lost and stumble in here).
http://nraas.wikispaces.com/page/messages/Chatterbox

Overwatch will not mind at all if you have aging turned off with the in-game option. The Stuck Aging Checks, etc. you are seeing discussed in the FAQ just won't fire so there would be nothing for OW to be worried about.

Where OW would do sometimes unexpected things is when another mod tries to impose its own alterations on the game's aging manager. AwesomeMod would be such an example; they can be used together but Awesome's TS2 Style aging option for example would not work right.