What AAA chemistry?
Let's assume that the "Cree R5" drop-in uses a driver that delivers 1A drive current to the LED (presumably an XM-L). For 3xAAA alkalines under load, you'll start at a nominal 4.5V (1.5V per cell), quickly (as in about 2 min) drop to 3.6V (1.2V per cell), and probably within about 5 min go below 3.3V (1.1V per cell).
The XM-L forward voltage is probably less than 3V at 1A drive (the datasheet indicates a Vf of about 2.98V, so call it 3V). So in theory, the Solarforce buck driver could run in regulation. In reality, I doubt it. The driver itself would have to have a small voltage overhead of less than say 0.4V. And then there is the parasitic resistance of the host light itself (spring contacts, battery-battery contacts, switch contacts). So if your cells are delivering say 3.6V to the driver, the driver voltage overhead plus the voltage drop from the parasitic resistance plus the XM-L Vf can't exceed 3.6V if you want to stay in regulation. I doubt this will be the case. And even if the 3xAAA alkalines do run in regulation, it won't be for very long (less than 2 min is my estimate).
If the Solarforce driver uses a drive current greater than 1A (e.g., 1.5A), then the situation is even worse. AAA alkalines will really sag under that load (since Vbatt ~ Vload, the current draw from the batteries will be approximately equal to the drive current) and it is even more doubtful that Vbatt will be high enough to reach regulation at all.
If the 3xAAAs are NiMH (e.g., Eneloops), you might be able to hold 3.6V for around 15 min. I still don't think you'll run in regulation at all, but at least the discharge profile of the NiMH cells are reasonably flat and will hold at about 1.2V per cell a lot longer than alkalines.
If you use 3x10440 Li-ions (AAA size), then you'll have a nominal 12.6V at the start. Even under load, you should have plenty of voltage (let's say 11.1V). and despite the relatively low capacity of 10440 Li-ions (around 200-300 mAh), you might get 30-50 min of run time and all or most of it in regulation.
Basically, IMO 3xAAA alkalines and even NiMHs are a poor choice for a flashlight load of over 1/2 amp if you expect a buck driver to stay in regulation. AAA alkalines and NiMHs just can't deliver enough voltage. AAA Li-ions are a lot better.
If your driver delivers 0.5A drive to an XM-L and you use 3xAAA NiMH, then I think you have a chance for some decent run time in full regulation. XM-L Vf is around 2.8V. AAA Eneloops probably can hold 1.25V per cell for close to 20 min. So you have about 1V of voltage headroom available and maybe you can stay in regulation for that ~20 min duration.