I bought F3 in the store, will F3 addons bought with steam work with that?

Download pages say it requires the base game "on Steam" in order to play, so I'd say no it won't work.

Price is the same on Games For Windows Live, I believe.

It's also cheaper to buy the GOTY edition online than to get all the DLCs. Generally a better option unless you only want one or two at the most.

You either need to buy the disc versions of the content (Operation: Anchorage/The Pitt, Broken Steel/Point Lookout, or the GOTY Edition) or purchase the content from Games for Windows LIVE. The Steam DLC only works with the Steam version of the game.