Hi Ben,
Overcharging, no, but a charger for 1.2V cells seems unlikely to charge lithium cells at all (they shut down when discharged to somewhere around 2.5-3V) unless the AA charger runs at a higher voltage than the cells it's intended to charge. I'll happily defer to Roger Caffin or a similarly informed electronics expert on that. Here's some "fun" reading on the care and feeding of Li-Ion batteries :-)
http://powerelectronics.com/portable_power_management/battery_charger_ics/804PET22li-ion-battery-life.pdf
On whether one can safely put higher voltage RCR123 cells in a SteriPEN, I'd seek their assurance that there's no potential to overdrive the purifier's electronics with over 7V, before trying. They may have protection built in, but it would be good to have a green light from the maker.
It's doubtful the SteriPEN will cycle reliably with partially charged RCR123 cells, at least with cold water. I've had the Aquastar fail to run with new, generic disposable cells with very cold water.
You might check the battery forum at Candlepower Forums for RCR123 brand suggestions. They're the go-to folks on what's available and especially, the brands to avoid because they might go "boom."
Cheers,
Rick