Is it bad wearing a sports bra to bed?
Answer your question first, it is totally ok to sleep with sports bra on, if you feel comfortable doing so, there is nothing wrong. Wearing sports bra while sleeping will not cause a cancer, there is no solid evidence showing connection between wearing bra while sleep and cancer.
On the opposite, if you do not feel good, take off your everyday bra or sports bra before go to sleep.
Will wearing a bra while sleep help preventing sagging?
The answer is no, wearing whatever kind of bra will not help preventing sagging. The point is whether you feel good with bra on or not.
If you like to sleep with bra on, or feel more security with bra on while sleep, I understand some women with large busts love to wear a bra for sleep, pick a sports bra, and definitely do not wear wired bra.