When you say your current rims are 26", I'm guessing that means 26 x 1 3/8", which is different than the 26" you find on current mountain bikes. (For details, http://sheldonbrown.com/tire-sizing.html).

The way I would check to see if 700s will work is by taking off a wheel and putting a 700 with tire on there. Alternatively, you could measure clearance. If my assumption above is correct, you'll need 16 mm more clearance at the top of the tire than you have with your current wheels. You'll also need to be able to move the brakes 16 mm up from where they are.

Wheels that size tended to have fat tires, so brake position is more likely to be the limiting factor.