I haven't broken a skewer on any bike, but I have broken a rear horizonal dropout just before a 400kim randonnee, but didn't realise it (bike fell over on the right side during a big wind gust).

I rode the randonnee, but wondered why the shifting into the big cogs was off, and why the chain shifted off the biggest into the spokes a couple of times. I didn't find the break until I got home from the event. It goes to show how the skewers can keep things together.

The other skewer-related problem was a groove worn into the dropout on the same bike. This was before a 1200 randonnee and the wheel wouldn't stay straight, no matter how tight I did up the skewer. I bought a new one from the only MTB shop in town. I eventually understood the problem, and smoothed down the dropouts when I repaired the broken one.

So... based on my experience, no, a pair of skewers would not be on my list of spares.