Is it possible to just drive through and see a few things and then camp outside the park?
Yes on the see a few things in the park. I've never camped outside but we were able to get a Kamping Kabin at the Mountainside KOA on somewhat short notice (although we had to cancel). There will be crowds, yes, but take a look at the park map and decide what you'd like to see. Old Faithful would be at the top of my list plus the geyser basins. Pick one section, see what you can see and if you have additional time just keep going.
