It's not recommended to exceed the 1C continuous discharge rate as the cell will heat up more, which can lead to the cell possibly exploding:poof:.
The driver on your dropin is based on AMC7135 linear regulators (search CPF for more info). AMC7135 linear regulators will maintain the rated output as long as the Vin (battery) requirements are met. The Vin requirements are the Vf of the LED + 0.12v overhead + host resistance. A single CR123 primary under load is roughly around 2.5v or less (depending on load), which is well under the requirements. Taking this into account the output on a single CR123 primary is probably going to be pretty dim (if it works at all). Since this is the case you will not get the full 2.1A output with a single CR123 primary.
A li-ion cell (LiCo, IMR) is better suited as their voltage under load will be higher. If you want to run the light on a single CR123 primary you need a boost driver.