Yes, public transit can get you to the resorts early enough for first chair. Quite a few of the resort employees use public transit, and a lot of them have to be there early enough to open the chairs for us so.....
Keep in mind that if you are staying in Park City, public transit will get you around in Park City, and to all of the resorts in and around Park City - Park City, The Canyons and Deer Valley (BOOOO!).
If you're Staying in the Salt Lake Valley, public transit will get you to the Cottonood Canyon Resorts - Brighton, Solitude, Snowbird and Alta (BOOOO!).
Getting in between Park City and the Salt Lake Valley is another story as far as public transit is concerned. I don't believe that there are any public transit options when it comes to that...