Yes, you should still have a good shot at being cast if you ask for 2 nights off. Obviously the more available you are, the more attractive of an applicant you become.
As far as using a sick night in order to attend the event..... do NOT do this. If they see you in the park you can and probably will be terminated.
Lastly, if you are cast as an Active Back-up, you will need to show up ready to work at least 5 nights in order to keep your employment with Universal (this number can and may change). If you are cast for FireCrew, you are expected to be there for every night that you said that you would be available. In most cases, FireCrew members only have a few (if any) days off.