You bet they can. They are all P. reticulata or a cross of those and something else like P. wingei. The fancy ones have just been bred to get a specific pattern or color.
If you put them in the same tank, you will not get fry that look like your fancy guppies but will probably get all types of fry.
It is fun to try and develop a unique strain of guppy. I don't think enough people are doing it but I wouldn't start by mixing a fancy guppy with a more common or "feeder" guppies. Start with a couple different looking fancy strains and a lot of tanks.
Guppies tend to want to mate with every fish in the tank. I've seen an Endler's livebearer (a guppy like fish) court a wild X. helleri. If you want, just put a couple of females in with a male in a 10 gallon tank. You can guarantee that you'll have fry in 1-1 1/2 months.