Yes, internet providers can block internet access to a Firestick, but in most cases they would have no reason to do so.
It’s much more likely that a cable provider would block access to specific websites or streaming sources rather than blocking all access to a device in your home. If you’re using Kodi on a Fire TV to stream pirated video, for example, then your ISP would block the source of the video rather than your Fire TV’s internet access.