Is this a thing at places like Two Sigma, Citadel, and others? If it is, what does the process look like?
Maybe if you have reaearch experience or a phd. Otherwise almost impossible.
It happens at small funds
Depends on the group. Certain groups have smaller distinctions between the two roles.
Usually not, no. If it does happen the process would be said applicant gaining relevant experience/credentials to be a quant and then going through the interview process just like anyone else.