Yes, you can do a full flaps Vfe descent. That wouldn't (hopefully) be in the context of an engine failure, but it can be done. I wouldn't do a 3000 FPM descent with passengers aboard, they'll probably decide to not fly with you again! Just remember that if you do that, and then actually have an engine failure while you're doing that, with full flaps already out, you've configured the airplane for the least good glide if you needed to. Setting up a base to final to flare with full flaps extended will take an extra layer of skill!
For years I fly jumpers, where a similarly fast descent was desired, I preferred to carry some power (to prevent shock cooling) and orbit down flaps up at a faster speed, A bit of G in a turn (if you're by yourself) will increase your rate of descent. That way the airplane is already set up in a good configuration for a glide if there is an engine problem.
And, for "normal" flying, a Vnav calculation....
I was right seat in the Twin Otter doing a ferry flight in 1985, and doing the radio work. We were number umpteen to land behind a long line of jets in Cairo. We were at 6000 feet approaching the airport. My Captain was a retired deHavilland test pilot. Cairo tower called me, and said that they had a break in the approaching jet traffic, if we could be down and clear in two minutes, we were cleared to land right now. I asked my Captain... As he reduced power, and smiled, he said "Yes". I accepted the landing clearance. The power smoothly came back to idle (PT-6's don't care about shock cooling), the plane slowed, the flaps went down as we continued to slow, and the nose went down, Then I felt the "braking" force, as he pulled the power levers into Beta range, and we rode some reverse all the way down to a nice landing - we were down and clear, from 6000 feet in less than the two minutes offered - not normal flying!