I think all the above answers touch upon your question, but hopefully we can answer it completely. First, what's your goal in riding? Do ride mostly road? To ride 'cross? Mountain bike trails? Anyway...
1) It is possible to buy a select few road bikes (700c wheels) and fit mtb wheels (26") on them. But you'd really need to get a road bike with disc brakes, and make sure the rear spacing is 135mm (mountain width), or choose the rare steel frame that has 132.5mm spacing to accomodate both road and mountain rear hub widths. Or, you'd build a rear mountain wheel with 130mm spacing, and that'd fit fine. Again, disc brakes would be necessary because rim brakes won't work due to the different rim diameters. The one exception is that there are a # of mountain bikes now that are 29ers, which means they use the same wheel diameter as road bikes. Those wheels would fit, depending on the rear hub spacing being compatible. But I really think you care more about tires, not wheels, and most road bikes and brakes will not accept wide, knobby tires.
2) Will it be a 'cross bike? No. I'm guessing you really don't care about wheel size but you're thinking more about what you need to ride 'cross. 'Cross bikes have pretty narrow, knobby tires. Some road bikes even have enough clearance on the frame and by the brakes to run some of the narrower 'cross tires (kenda makes a tire called the kwick that is pretty narrow). in terms of geometry, the road bike would be closer to a 'cross bike than a mountain bike, and won't have the front (or rear) suspension that most mountain bikes come with
3) if you just want to try 'cross, and own either a road or mountain bike, either can work, and both have advantages or disadvantages. there are narrow mtb tires (1.5" or less) out there that are great for 'cross. the biggest downside will be the extra weight of a mountain bike.
4) if you're buying a new bike, just buy a 'cross bike! you can put slicks on it for road riding, knobbies for trail riding, and of course, be all set for 'cross. find one that offers a lot of clearance for wider tires if you want to use it as an mtb at times.