Yeah, they run in the wet. They can cancel in the wet too. They will pretty much always run in the wet at a natural road course. A lot of our races, though, are held on oval tracks where part of the oval is used and a sort of road course section is carved out of the infield. If you've watched the F1 USGP at Indianapolis, you get the idea. It can be dangerous to run in the wet at those venues because the oval portion has no run-off, just a wall.
Rain doesn't happen that often. It's a short season, and they've been pretty lucky over the last few years, though there was an interesting wet race at Road America a season or two ago.
Here's the section on inclement weather from the AMA rule book for the Superbike series:
6.7 Inclement Weather / Unacceptable Track Conditions
a. Events may be conducted regardless of weather conditions.
b. In the event of rain or other conditions, it may be necessary for the
Race Manager to adjust the order of the event schedule, the length of
races, practices and qualifying sessions, or to stop the program
completely. Should this occur, the Race Manager will make every effort
to resume the schedule in a timely fashion if conditions improve
sufficiently. See Wet Start Events (6.18).
c. If a meet is stopped due to weather or other conditions, riders will be
paid for any purse-carrying events which have been completed.