Your hub is probably spaced at 135mm. Most road stuff is either 126mm (old) or 130mm (newer). If you get a wheelset with solid axles you can simply at a couple millimeters of spacers to each side of the hub to account for the difference in width.
The front wheel will most likely clear the fork crown and downtube, but the rear wheel may hit the chainstay, or seatstay, bridge. Also, unless you have disc brakes, you won't be able to make your current brakeset work with the larger diameter rim.
In other words: No, 700c wheels probably won't work.