Yes but the MiG-17 wing sweep, slight length increase and new tail (moving the elevators back from the wings) was to solve that issue. The MiG-17 did not have this issue like the 15, that is the pilot would probably have to try to induce it.
In fact, you can induce this problem on any T-tail if the layout allows you to block airflow over the elevators with your main wings. That's how you do it. And most will with some hard alpha at the wrong time.
The reason the F-104 did it particularly, was the chord was gigantic. You didn't need much alpha to lose your elevator, which induced longitudinal instability. There's plenty of in flight footage of them doing it.
The MiG-15 didn't do it as easily, you need to be at high altitude so you're at a lower IAS compared to TAS. Then you need a little bank, kick some rudder, pull too quick and hard on the stick and there you go, no elevators, flip, no rudder, spin.
But two things should happen for it to occur, you have to be a very high altitude (up near ceiling), and start doing BFM like you're in a dogfight. It'll do the spin, there's F-86 pilot reports on it (chase to high alt, MiG spins, kill recorded without a shot fired), common enough to be either true or a conspiracy. I won't even mention what I think of conspiracy theories.
This was corrected in the MiG-17, it was part of the design requirements. TsAGI says "to correct unsatisfactory factors" (winchester). The RAF dealt with this on their T-tail jets around the same time by moving the elevators a bit forward of the fin. Another way is to play with main wing sweep and moving the wing box in conjunction but that messes with general handling qualities, you can lengthen the vertical stabilizer but you may have structural issues (these love cracking around the base).
There's also a Wright-Patterson report on comparative flight testing of a captured MiG-15, also discusses it.
Once again however, an experienced pilot should never really have this problem. It's just you have to know the plane limitations and enforce them as a pilot, the plane won't tell you and it won't stop you.
US test pilot conclusions was that an inexperienced pilot or someone who panics would have this problem, but it is there to have.