It is ok, and the H30 & SC30 were designed to run on rechargeables. I have the SC30, and only run RCR123's in it. The light is close to 2 years old, and still works great.
I can confirm the H31 works on RCR123s as I had a protected Ultrafire 880mAH 3.6v cell and once it was time to recharge I had it stuck in the body and needed to glue a pencap to pull it out. So be careful with thicker protected cells in the H31. I do run the Tenergy LiFEPO4 3.0v RCRs and they are the same exact size as CR123 primaries and also only 3.0v. They run a long time and I can't be more specific as I use low and low 2 the most so my cells last me for months using the light at night mostly for short <5-30 minute periods at a time, pretty regularly every week.
i've never had problems using 16340's in my h31..I use protected trustfire flames and they fit perfectly..they are commonly accepted as larger than normal from what i've read..haven't measured runtimes, but I have never been disappointed with it running out of juice prematurely..for the lumens it produces it seems to be very efficient on 16340's..