Here are some observations from more than a decade in the automotive tire business:
sealant can indeed cause an unbalanced condition. I learned that in my early days trying in vain to spin balance a tire for a very long time before I finally ended up telling the customer I couldn't get it to zero out, and he admitted he'd put Fix-a-Flat (specifically that brand) in it.
They do work. In fact, they can work so well that when you take the tire in to get it repaired, the tire tech might never find the puncture if you've removed whatever made the hole.
Slime sort of gels and does so fairly quickly, but it would still take days to dry out. Fix-a-flat can take weeks.
They can corrode alloy and steel wheels. The steel rusts, but that's not too big a problem. Alloys however can have chrome plating or clearcoat start to peel, which can result in constant bead leakage.
Tire techs the world over curse you enthusiastically if you don't share with them that you've put a sealant in the tire, and they manage to get it all over themselves, their tire machine, and the shop floor.
I cannot speak to its effectiveness in a tubed tire since I just don't get many innertubes crossing my path, but the advice about removing the foreign object from the tire/tube is sound reasoning, and I don't see why a viscous sealant like Slime couldn't get the job done.
All that said, I have used it, I will use it again if need be, because sometimes that's what it takes to get on up the road and get the tire repaired or replaced.
You can call me Billy. Or Luci. But don't call me Shirley.
2011 Cross Roads, crimson red
Lloyd'z ATS, IAV, VFC-III. Vic "High Performance" air filter. Ness Big Honkers. Funsies.
2015 Vegas 8-Ball