It really depends on the drop-in being used. a Cree Q5 or R2 bin emitter is only good for about 4V tops (depending on Vf) so it all depends on the electronics included on the drop-in and has nothing to do with whether it is a Q2 or Q4 or Q5 or R2 or anything.
I did a little searching around the web and found numerous reports of the solarforce drop-ins being used on pairs of 3.7V RCR123 cells. I'm not sure what their maximum voltage input is, but it's high enough for your intended application.
unprotected cells are not what I would recommend, especially if you have limited experience with loose li-ion cells. Keep in mind that in consumer devices, li-ion cells are closely monitored. The charging is terminated properly, and the device is designed to shut off before the cells are completely depleted. We have a false sense of security generated by the numerous consumer devices we surround ourselves with that use li-ion power storage solutions. Loose li-ion cells, when over-discharged, are much more susceptible to exploding while being charged than cells that are properly maintained by protective circuitry (as the protected cells would not have been over-discharged to begin with).
Most drop-ins that support relatively high voltage inputs, use a buck style regulation that will provide maximum output until the input voltage drops to around ~4-4.5V depending on the Vf of the LED and various other internal characteristics of the module itself. The problem with this, is that your light will appear at maximum brightness while your cells are closing in on ~2V per cell, which is way below the ideal discharge voltage and *could* lead to cells that are less and less safe to charge with each cycle.
My suggestion for safe use of these cells, would be to take voltage readings of these cells at various points through a "test" discharge. Run the module for 15-20 minutes first from a full charge, allow it to cool off, and then resume testing with 5 minute intervals until the cells are down to around 3.6V-3.7V open circuit. then reduce intervals for testing to about 1 minute each until the cells are reading no less than about 3.5V open circuit voltage. Then add up your total runtime for all the intervals, call this "100% discharge" time. Multiply your available total runtime by about 0.75 (75%) and make this your "target" maximum runtime per cycle.
Keep in mind that you can top up li-ion cells at any time you desire. Shallower discharge cycles re actually healthy for li-ion cells. For example, lets say you calculate a total available runtime of 50 minutes. You should try to make a mental note never to run the flashlight for longer than a total of ~37 minutes on 1 charge, but if you use it for 5 minutes, there is no harm in topping off the cells in the charger and starting the runtime clock over again.
If you follow this guideline the use of the unprotected cells will be relatively safe and I would see no reason for major concern, but if you make a habit of running the cells down until the flashlight is dim, you might consider a re-investment in protected cells.
Eric