I just tried this a few days ago on my (low Eb) Selmer bass. It's so much better!
I was having trouble navigating the inner RH pinky keys (i.e., RH low F# and low E), and found it difficult to reliably keep enough pressure on the RH ring finger key (low G) while playing any of the RH pinky keys in quick passages.
When I finally removed the thumbrest and tested to see where I might reposition it, I was amazed at how much better my right hand felt without the thumb rest. For me, it works equally well when standing (with the bass supported by a strap) or seated (where I use the strap in combination with a peg).