Absolutely, private observations have a reduced value for research. That isn’t to say that some observations shouldn’t be private, but there’s definitely a trade-off. Personally, if there’s an observation I feel is so sensitive that I would want to make it private, I generally don’t even post it on iNat.
The question and related ones (about IDing private observations) have come up on the forum before and have good info, examples:
https://forum.inaturalist.org/t/if-location-is-obscured-is-the-observation-still-useful/46522
https://forum.inaturalist.org/t/does-obscuring-your-location-affect-the-chances-of-getting-research-grade-ids/59899
I can confirm that private observation locations are not exported to GBIF - otherwise it would pretty much defeat the purpose as anyone can make a GBIF account and download the info. Users can choose to trust other users or projects with true location info, so it is possible to share that location info for private observations via iNat. As such, there’s some potential utility there, but this only applies to a very small proportion of iNat users.