I tried one (Battery Space) with an OLD ARC LS (first run # 2294) Kind of scary to do so, but it survived about 25 minutes of total run time, 2 to 10 minutes at a time with no apparent problems.
Didn't get MUCH hotter, but WAY brighter than with a Standard (Battery Station) 123 cell.
Here are a few measurements:
New Battery Station 123 lithium primary:
3.23V no load
470ma current draw,
215 LUX (1 Meter)
Battery Space 123 rechargable: (It sat around about 24 hours after its first time charge):
No load voltage: 3.998V
Current draw: 351.0 ma
325 LUX
After 10 minutes, 5 minutes on, 5 off, 5 back on:
293 LUX
After about 20 minutes intermittant:
3.6V no load on battery,
375.0 ma
257LUX
I'll probably be nervous about burning out one of my old ARC LSs using them, but it is nice to know that it does work for a while at least in my particular test light, and puts out a significantly higher level of brightness.
Your results may vary.