Yes. If his chamber is tight, he could get about 3150 fps from a 20" barrel, but if it isn't it might be anywhere from 3000 fps to 3150. Let's say 3075 fps as an average number. That will put the RPM at about 243,000 as Mal suggested. That would be a lot with a 30 cal bullet or even a 27, but with a 22 caliber bullet, given its narrower diameter and much lower mass near the surface, the centrifugal effects and core stripping forces will be much smaller and unlikely to affect it, IMHO.
The JBM stability calculator puts the stability factor at around 2.2 in standard conditions, which is well within Sierra's criteria of 1.3 to 3.0 for hunting accuracy and I've seen 168-grain MatchKings shoot half moa at a stability factors of over 2.5, so if the bullet is well made as to axial mass symmetry, it should still shoot, even if ideal stability factors for peak accuracy ar around 1.4 to 1.7.
To answer Mr. O'Heir's question, the load came from the Nosler load data (available both at their website and in their manual) and is the starting load. The Nosler data uses a 24" Lilja barrel that gets Nosler 3300 fps. If you cut that same barrel to 20", Quickload says the velocity would drop to 3147 fps, which is where I got my "about 3150 fps", above.
I note the Nosler data barrel uses the SAAMI standard 12" twist.