Yes, road bikes are different, and many road bike frames are not going to be too good for 'cross.
The biggest problem will be tire clearance. Many road frames are so tight they won't clear even a 700x28c between the stays or behind the seat tube. You'll have a hard time fitting 'cross tires on such frames. And even if you can get the bigger tires on there, you won't have cantilever brake bosses, which are the usual solution for clearing bigger tires.
The next problem is "rise" below the bottom bracket shell. 'Cross bikes have more rise, for increased ground clearance.
Also, you have to look at cable routing. Shouldering the bike is usually necessary at some point in the race, and cables routed along the bottom of the top tube can make that problematic.
If there's no 'cross racing available to you, why do you want a 'cross bike?
Training: 2002 Fuji Roubaix Pro (105 triple)
Commuting/Daytripping: 2001 Airborne Carpe Diem (Ultegra/XTR, touring wheels)
Commuting/Touring: 2000 Novara Randonee (Sora/Tiagra/LX, fenders, lights)