Configure Time Machine after reinstalling Mac OS to take previous backups into account
Yes. The command line utility can assist
man tmutil
You'll want to use the verbs inheritbackup, setdestination and/or associatedisk to point out the pre-existing backup you wish to adopt by the new Mac/OS.
This is covered in very nice detail on the help / manual page - pay attention to the section after this sentence:
A concrete example of when and how you would use associatedisk: