Almost definitely no, at least in my district. Target is big on scheduling to the needs of the business, and Sundays are often big days for stores. I wouldn't hire a TM who couldn't work Sundays, let alone a TL, especially because as was already mentioned it wouldn't be fair to other TLs.
Depends heavily on the store. One of our GSTL's is a college student, so he pretty much has a set schedule. He has class 3 times a week, 2 of them are his day off and the always closes on the third. One of the SLTL's also has a limited availability.
It is certainly possible to have limited availability as a TL. Several do in my store, hell, the STL won't work Thursday nights during the winter because he volunteers as a ski instructor.
However, I believe limiting your availability on Friday nights and the weekends is non-negotiable as business needs dictate that supervisors need to be available during peak shopping times.
I never work Sunday morning as a Sr TL. I also have off every Tuesday and Thursday for School with only Friday being fully open. I do work every weekend but in the end, I always know what is going on!