The Quark AA² R5 works on .9-4.2V (depleted AA NiMH or Alkaline - fully charged LiIon). The 123² works on 3-9V (2xAA or CR123a primary - or 2 fully charged LiIon). IIRC, all the parts should be physically interchangeable. As long as you're not using the AA² head on more than a single lithium primary or LiIon cell, it should be fine. Just keep in mind that running a flashlight on multiple LiIon cells has inherent risks if the cells are unprotected. Personally, I'm not comfortable running multiple protected LiIon cells, as there's still the possibility of damage occurring, or at least triggering the protection, which would render the cell(s) useless until reset in a charger. The risk is slight, but the potential PITA is greater, and not worth the hassle if the light will work fine on a single LiIon cell.
There might be an issue with fitting 2 14500 cells within the 2AA battery tube. They're longer than a typical AA battery, but they don't have the "nipple" either. They might fit, they might not. But as far as frying it, as long as you're using the 123² head, you should be fine. But compared to running a single 14500 or R123A, output won't be any brighter, just longer.
Looking for a GEC Bull Nose sodbuster in Nifebrite acrylic. If you have one to sell or know where I can find one, let me know.