It’s been mentioned that the light functions on 1s, although I don’t think anyone has tested to see where it drops out of regulation. Let’s assume 3.65v, since that’s the XM-L2 vF at 3A from djozz’s chart plus the 0.25v sense voltage of the driver. Everything above that should regulate. This is a buck driver, so higher input voltages will require lower input currents. If you want to use alkaline in a pinch, try to keep the voltage as high as possible (within reasonable limits).
With only 4*C (alkaline) I don’t think “High” would work for very long. Maybe about 20minutes. Ref HJK’s Panasonic Pro Power C review here. In order to get approximately 1hr of battery life in High mode I think you’d want 8*C.
You could also consider using 4* Lithium AA with a sleeve. If you made caps for the sleeve, that could easily be stored alongside the light with batteries installed in it for an emergency. I think that 4*AA (Lithium) could do almost an hour in “High”! See HKJ’s Energizer Ultimate Lithium AA review here.
Oops, I forgot to account for dropout voltage while doing the 4* runtime calcs. Lithium is probably about the same, 8*C is the same as well, but 4*C may suffer a little. These are all quick and dirty things anyway, back-of-the-napkin type math.