what happens if you drive with a clogged up air filter?

I imagine it will run richer and richer until it stops. Just like putting your finger on the carb. Performance will get worse.

will it do any damage to the engine?

It will actually overheat and lean out as a result of the increased heat. Can't explain that with physics but I've heard it happen like this to several people whose filter got clogged up in dusty races. They lost power and at the end of the race the engine was at 160°C .
The best thing to do if that happens is to rip the clogged up outer filter off during pitting and finishing the race with the inner filter.

When I run in dusty conditions I change the complete air filter every 4-6 tanks and at races before every qualifier or final. You can also run the outer filter with only very little oil or none at all so most of the dust won't stick to it but then the inner one won't last as long as more dust will get to it when the outer one isn't oiled.
One other thing: Never ever wash the inner filters. They might seem clean again after washing them, but they aren't. I use filters with surgical quality foam (against which even the Mugen filters look like yellow packing foam) and when you try to wash them they never get as white as before. That says a lot to me.

Don't know. I was guessing what might happen and if I am right it would just run like crap.
However, if you continue to lean it out because you think it runs rich I think it will wear out due to lack of lubrication. See ti this way, a resticted filter will have the same effect as running on very high altitude which means less oxygen, which in turn result in less fuel being burnt.

i always notice right after i oil my filter a whole bunch of dust gets stuck to the outside of the foam. i have a single stage filter (just one big foam). is this bad, or is it just normal? is it suffocating the carburetor because a layer of dust is over it?

Dust sticks to oil so there is nothing you can do about that. Putting on a 2'nd stage filter will help some.