I don't actually own a Prothingy, but I'd have to say it would. The main variation in thickness in the batteries is the wrapping, and the maximum variation in the length is about 5 mm and that is for a protected battery. The voltages of course will be the same.
What I do have a problem with is the overall performance of some or most of these higher capacity batteries is not really that great. There's a lot of trade offs with the battery technology at this level. While the available maximum current may be greater, we don't really need it for a regulated device like the Provari and Vamo and the actual performance in a PV may not be any better than the lower capacity batteries. There was one test done by someone over on the flashlight forums on a high capacity battery which show the actual available power before the 3.2 V cutoff was less than the 2000 mAh I just bought from fastech (which happens to be one of the cheapest and best performers I could find after a lot of hours researching batteries).
There's a review of batteries and lots of good information here: 2012 Battery test/review summary. Higher capacity figures on the batteries does not actually equate to better performance, or even the equivalent performance for out purposes.
I don't see the advantage of paying for a performance feature that we don't really need when the trade-offs are likely to be actual run time in a PV and especially the long term lifespan of the battery. My experience with paying for the highest performance batteries and the problems associated with them has convinced me to stay with the cheaper lower rated batteries that have more reliable and safer technology.
The batteries I just bought are only rated at 2000 mAh, but deliver most of that power before the 3.2V cuttoff. If you dig up some of the discharge curves on these higher capacity batteries, a lot of that extra runtime is below the 3.2V cutoff, since the rated discharge is to dead flat or 2.7V, which is pretty much the same thing.
