"This may sound stupid, but is there a way to check to see if the floats...float?"

It sounds pedantic but you remove the float from the carb and put it in a tub of something. Water and Gas have similar densities so you do not need to test in Gas but make sure the float is dry again before you put it back in the carb.
I have had a sinking float, not a fun problem to diagnose and not fun to fix on a brass float [vintage Land Rover]
Welcome to the vintage vehicle addiction. As others have said find and use the online brain trust specific to your vehicle, it/ they are worth their weight in diamonds/ gold/ crude oil .