Time Machine won't delete old backups until it thinks it needs more space to store a new backup. However, you do not get a warning before the deletion happens - only after the deletion deed is done, does the warning pop up.
You could trust this in the short term, however starting a backup of a cleanly reinstalled Mac is one way to have the system estimate it needs 100% of the side of the drive to start the next backup.
I would not connect that drive to the restored Mac until you can turn off Time Machine and then copy using Finder one of the old backup intervals you wish to save. You could just set the old drive on the shelf or get a new drive to store the "long term" snapshot.
Basically, you don't get notified before the deletion happens, so if you want to keep files, you need to take action now if you are not 100% certain that there is enough space to prevent automatic deletion.