Will BTT ever 'expire' for those who choose 2 years?

Big Sur was just released. I'm wondering if there will eventually be an OS update that causes those who bought the 2 year license to not be able to use the app. I understand I won't be able to get new updates, but is it possible that I need one in order for BTT to work?

That is very possible because often things need to be adapted for new macOS versions. However for Big Sur most things still seem to work for older BTT versions!
You can only be sure you can use that version of BTT forever on the macOS version that was available when you purchased your license.