Hi, welcome to the forum :D
I suspect this really ought to be in the Tech forum - the Pickups forum is usually for "about BKP pickups", so be warned it might get moved by the moderator man :D
But to answer your question - I would have thought it is very possible steel wool can cause a short if it gets inside. It's always best to get the pups out of the way before putting steel wool anywhere near the guitar...
If it has got in there, it'll be a pig to get it away from the magnets.
The "getting sound but no multimeter reading" sounds weird, but I'm not an expert user of multimeters and what the readings mean...