The reality of recoil is that most shooters are done by the time they reach the 30-06/7 Rem level and its best to work up to that. By the time you get to the .300 Win Mag you've lost just about everyone. That reality is largely mental, and it can be overcome. Those that do cross-over whether comfortably or eventually just make a ramp out of empty casing and stroll over the hurdle, usually can just keep right on going into calibers that really kick. Things that make a .338 feel like a 243.
So the answer to whether a shooter can handle the small and medium magnums is probably not. If the the question is whether a dedicated shooter can learn to like it then the answer is yes, absolutely. If the question was whether they will actually do it instead of of talking about it the answer changes back to probably not. Recoil is mostly in your head. If it wasn't, then how would people ever get used to it? It's not like they get a callous on their shoulder after the 100th box of shells, or develope some form of permanent numbness. The only thing that changed is their perception; their mind has gone from thinking it is under some sort of attack to learning that it is actually no big deal and they will still be standing there iuninjured when it's over.