For the destinations you listed, yes. Look at google maps or whatever you use. Then look at the distances from where you will be staying to Mt Lemmon, Gates Pass and any other destinations you have. Look at the elevation changes as well. Mt Lemmon is around 7800 ft, Tucson is around 2500. I have met people who have ridden up and down the mountain. So it is possible. But I'm not ready for it myself.

BTW: If you go to Gates Pass you might as well go on to the http://www.desertmuseum.org/. It's worth it in my opinion.