You might be able to get away with it for a little while, but eventually it will end in a train wreck. After while, you will no longer be in the same measure as the drummer. And in rock music, the drummer is the conductor. Everyone gets their beat from the drummer. If your drummer starts to run (get faster), so will the rest of the band. The only place I could see this working is in really heavy, non-melodic Jazz.
However, it is possible to make one time sound like another. Take the drum beat for the song "Kashmir" by Led Zepplin. If you are not counting beats, it almost feel like Bonham's playing a 4/4 beat, but he's actually playin in 3/4 time. On the other hand, you can also make 4/4 sound more like 3/4 by "swinging" the tempo. It's all a matter of accents.
We're used to hearing the accents on certain notes, and in rock music in 4/4 time, we're used to hearing them on the 1 beat and the 3 beat. If you accent the notes in a different place, you can give the song a whole different feel, and give the allusion that you are playing in a different time scale.
If you were to do this though, you couldn't do it with a drum machine. You would have to try this out with a live drummer.