Short Answer
The worst that could happen could be a catastrophic failure, but like everything else in life, it is not black and white. There are shades of gray in between no problem and disaster.
Longer Answer
Interesting information here from one of your fellow Commonwealth Countries:
http://www.gma.vic.gov.au/hunting/duck/hunting-methods/non-toxic-shot/possible-effects-to-guns
Long Winded, Opined, Answer
A lot of variables are at work with steel, what type of gun, what type of steel is the barrel made of, what condition is it in, how much do you plan to shoot steel? If a shotgun, how is it choked? And others.
The problem with steel shot is it is nearly as hard as newer modern barrels and harder than older ones, so the older they are the more damage. Logic would dictate that that scoring would be worse is softer barrels and longitudinal grooves cut in the barrel are going to weaken. The question is how much and how long before it fails? (I'm thinking Russian Roulette here)
Additionally, choked guns provide an additional danger by raising the pressure in the barrel. Steel shot, being much harder, does not compress as much as lead going through the choke. It has to realign itself passing through. This backs things up like a banana in a tail pipe, increasing pressure, which can lead to ringing in the barrel or worse. I rather think this is why Pedersoli, in their manual for their ML guns, recommends no tighter choke than improved cylinder when using steel shot in their shotguns.
http://www.davide-pedersoli.com/uploads/supporto/14AVC_INGLESE.pdf
(its specific to Pedersoli, but lots of good general info on all types of ML guns, cleaning, assembly etc.
Another set of variables are reasons to be using steel. There are, I'm sure, uncountable times throughout history where just about anything that'll fit has been jammed down a gun barrel. (Check You Tube).
If you're up against the wall, with only your treasured custom built Bess, imminent danger closing in, that requires deadly force, and your mindset is survival, not remaining PC to the death, I'd grab a handful of pea gravel if that's all there was.
If your looking for a way to keep shooting while avoiding an agenda driven Progressive ban on lead, I'd look at one of the tungsten-matrix, bismuth or other non-toxic options, like Hevi Shot. They are available bulk if you plan to shoot a lot, or open up some modern shells and take the shot out if you're going to shoot a little. More expensive, but that's part of the Progressive agenda.
If you're just doing it to save money, by buying a sack of BBs from the discount store, or just for S&Gs because you have a sack of ball bearings laying around and want to see what happens.... Son, you're on your own. Just put up a "Darwin At Work" sign to warn the rest of us to stay clear, if we so desire.