It should run, but it's not supported and we don't test older versions with newly released OS.
Note that with Catalina, applications need to be signed by the developer "notarized" for Apple for them to install. We have gone back and re-built the installers for KeyShot 7-9 for Catalina to comply with this, but not 1-6, so you would need to go into your system settings and by-pass the Notarization for it to properly install.