It's pretty hard to get a 3.7V RCR123 into an L1 body, the body opening is constricted in diameter a bit and rechargeable cells seem to be a bit fatter than primaries.
However I think I've heard of folks getting 3.0V rechargeable cells in there and having them work fine. Maybe some of the 3.0V cells are skinnier?
I've had a cree L1 head on an E1 body running with a 3.7V RCR123 cell. It was unregulated and considerably brighter (I'd say overdriven), but it didn't go