Yes, for example I married my partner who was on an F1 visa, which is a non-immigrant visa, and we were able to easily adjust his status to the GC (this is faster than the K1 process)

That’s useful to know. One difference for my situation is I’d like the H1B1 holder to be able to continue working during the application, but I have heard mixed information on how feasible that is. The H1B1 needs to be renewed quite frequently but may not be renewable while you have an adjustment pending.

There are potential issues with being in H-1B1 status and applying for a green card but they revolve more around timing - so, for example, if you entered the U.S. on an H-1B1 visa (as opposed to H-1B), which is not a dual-intent visa, then you would need to wait some unspecified period of time before applying for a green card to avoid being "charged" with immigration fraud at the time of your entry in H-1B1 status. Also, after filing your green card application, while you could continue working on your H-1B1 visa, you wouldn't be able to travel internationally on it and you wouldn't be able to travel in general for an extended period of time unless you had a family emergency abroad.