Yes, the cap's life should be as you say, and yes this is an electrolytic cap.
The main thing to consider is the applicable ripple current, that governs the
cap's physical size so although you can get 10,00uf caps rated at 35 or 50v
that are very small, you really should use one's with a large ripple capacity
if you intent to run battery-less.
I would suspect a polymer or similar cap is what is embedded in those regulators
as they are small but i don't know for sure.