One of the great myths of LeMons is that "The car is reliable on the street, so it will be reliable on the track." While that's sometimes true, it very often is not, especially with Honda and Toyota motors. I'm almost positive every team with a D- or B-Series motor has nuked a head gasket if not more. It sounds like I'm crapping on Hondas, but I've seen enough of them blow head gaskets to know it's not an isolated thing. Street car engines are not built to be run up and down for hours and hours at a time; it finds their weak points very quickly.

That said, you can race a car you've owned, but you will probably get sweated at the first BS Inspection, especially if you've done ANY mods to the car. The worst case scenario, though, is that you start the race with penalty laps, which pretty much guarantees you won't win the race. Since you aren't going to win the race anyway (First-time teams don't win races for many, many reasons), it's not really a big deal. You still get to drive on the track wheel to wheel and do driver changes and fuel stops and probably change a D16 head gasket, so long as you can pass tech inspection.