That's something I've considered. Saami lists the chamber pressures of the following rimfire cartridges as follows:
.22 short- 21,000 psi
.22 LR- 24,000 psi
.17 HMR- 26,000 psi
All are well under the tolorances the AR platform can withstand, as the .223 Remington has a chamber pressure of 55,000 psi, which I shoot from my .223 wylde chambered AR along with 5.56.
There's another .17 variant, I think .17hm2? I can't remember, anyway, it's the same length as the .22 LR, and probably nearly the same in pressure and would probably function perfectly in a .22LR mag, but I don't see much point in doing that, I'd just shoot .22LR. The .17 HMR is the same length as .22 WRM if I remember correctly.
If the barrel clambering and mag were correct, the question is whether the .22 conversion bcg could withstand the extra 2,000 psi. The AR platform itself can handle it no problem, but I don't know about a .22 bcg. I assume they're only tested to withstand the 24,000 psi of the .22 LR, not the extra 2,000 psi. Hmm.