General musical training will not be genre specific, with the exception of classical vs. modern training.
You question is a little off topic for a general music question as it is based on (1) being an amateur, and (2) some preconceived notion about being a professional.
So, I'd throw the question back to you in a different context...
Surgeons all have medical and surgical training so can an orthopedic surgeon operate a heart or do they need special training?
Perhaps not a fair question, more like a false equivalence. But it illustrates the point. All professional musical training will focus on chop building, reading, performance, etc. To get through a curriculum you need to prove you have chops. But these chops do not prepare you for the idiosyncrasies of a specific genre of music and the demands it places on the musician. So a better question might be can a professional drummer play as fast as...
One potential false implication in your question is that death metal drummers are not professional, though I don't think you meant to imply this. For all we know the drummer for Decapitated or Dying Fetus went to Julliard. Professional training teaches the musician to move optimally, without wasting energy, like Bruce Lee's 1 inch power punch. You don't spend all you effort moving as fast as you can you learn to move gracefully and speed comes with that.
I would venture to guess that a professional percussionist could tap out a death metal fill or rudiment at speed. They may take some extra practice to become familiar with the specific fill but in theory there is no reason to expect they would choke. An altogether different issue is whether the average working drummer (with a three or four piece kit) would be able to easily play on a Chad Wackerman or Neil Peart kit. Some metal drummers have kits like these. That is like learning a new instrument and may take a little while to get used to.
Going the other way, a lot of "famous" rock stars, while talented, came up playing one type of music and are self taught. As a result many don't venture away form their roots. There are some pretty well known rock drummer that couldn't play a simple back beat or a swing grove. So I'd place my bet on the pro adapting to metal rather than a metal specialist playing something simple that isn't a fast 4/4.