Non-indexed shifters (ones which don't click) will operate virtually any derailleur. If you're not using indexed shifting, any derailleur will shift any set of sprockets, provided it a) clears the largest sprocket and b) has enough range of motion to go right across the cluster. A) is the issue for a road derailleur on what is effectively an MTB transmission. As for the 700c wheels in your garage, the front should fit straight on, seeing as the bike came with 700c wheels. Whether the rear will be a drop-in replacement depends on whether the width of the hub across the locknuts matches the spacing of your rear dropouts, if it doesn't, it's a little more complicated. If you do fit it, you're likely to need to readjust the limit screws on the rear derailleur.