I had a package waiting when I got home, so I put together a simple test circuit using an extra piece of copper clad board. It's basically the power supply circuit portion of this project with a momentary switch, a dropping resistor, and three white LEDs in parallel. I had to add a bit of kapton tape under the battery as I hadn't taken out enough copper and I was getting a short circuit:

The LEDs are pretty bright, so this is the best action shot I could get:

I checked--the battery voltage sags to around 2.2 vdc when I hit the button (and dropping...); however, the output rail is steady at 3.3 vdc. Voltage drop across the resistor suggests the LEDs are pulling ~40 mA. The coin cells should have 240 mAh capacity, and I should be able to use them down to ~0.8 vdc with the boost converter. I'm going to wedge the button on and see how long it stays lit--any guesses?