Yes, you can screw it down, but as several have mentioned, it throws the geometry of the guitar off. With bolt necks you can shim the neck to fix this, but with set necks you can’t. While it will be off, that doesn’t guarantee that you won’t be satisfied with the results.
Tonally, you will get more bottom end. Somewhere between low mids and lows, you’ll get more bottom end. Exactly where it comes depends on all the other factors of the guitar.
If you do it, you get all the advantages Aahzz mentions... quick, accurate drop D on the fly, no “give” when bending, no whole guitar out of tune if you break a string, etc.
The way to get the positives and avoid the negatives, is to block it below. No geometry changes, you can still go down with the vibrato, and all the positives of a decked vibrato.
I prefer decked. I bought guitars that way (Wolfgang, Axis), decked every strat I’ve had, but never done it to a set neck including any of my PRS guitars.