No, you should not have to re-install plug-ins.
You might have to use Plugin Manger to point to the locations where your plug-ins are installed.
Don’t forget that you can’t use 32 bit plug-ins in Cubase 9 without using jBridge or similar.
You also might want to search for your plugin names with the term Blacklist to see if other users have had issues as Cubase 9 blacklists plugins that it thinks might cause problems (including all 32bit ones). There’s also a Blacklisted Plugins subject here in the forum that might be worth browsing if you haven’t already.
Finally, you will still be able to use 8.5 after you’ve installed 9, it’s a separate installation and both can be used under your new upgraded 9 license.