My advice is go to the drum show. That's what I would do. Those schools always need people to come in so they can get experience setting up the mics, getting the levels on the mics, eq'ing the instruments,
Etc. I am sure this would not be your only opportunity to do something like this. There going to have you hit each drum to set levels, then play a beat to check everything. Also, sometimes but not always,the drums may sound like crap in the drum booth but great in the control room. Most studios don't want you to tune anything because they usually have a sound all dialed in on the studio kit. I think the most important things to bring would be your foot pedal and seat.
Maybe your favorite snare. I think they would be open to that. If they want to record to a click, you have to tell them the tempo of the song so they can set the beats per minute / tempo. Or they can give you a click and the band can decide what speed sounds right for the tempo of the song. When you Start recording give the click a couple of measures and YOU count it off and all start together. I will use the audio click or have a cowbell sound for the click with a accent on the one. You will also hear the other instruments in your headphones, Or they may record you without a click or both ways. Just have fun. It will be a enjoyable and good experience . Hope this helps some.