just tested it (with my old serie 4) and the 7.2 beta profile could be installed to the watch, without running beta on the phone (which runs iOS 14.2). so far not seeing any difficulties.
From ancient experiments (with watch OS 5.x and 6.x some time ago) i know for sure, that this might result in 'glitches', like not being able to configure a particular watch face for example, that is new in the watches beta OS, but not 'known' by the phone (for example). As this could be tolerated, maybe other options, that were introduced with the beta, might not be available in the phone as well.. so this is (for me) resulting to the answer:
yes, watch can run beta, while the phone is still on public/production version,
but if this is a good idea (because of possibly missing config features in the phone), is a completely different question
As the phone can be restored from a beta back to the latest public version by the owner, it is important to be aware of the fact, that this is NOT possible for the watch! Downgrading the watch from beta software back to production version can only be done by APPLE (incl. sending the watch in and maybe paying bucks for it).