I would be hesitant to put a tanning shelf in a vinyl pool. I don't know that I've ever seen it done before, but could be wrong. You won't want to put any chairs in it, for fear of tearing the liner. And an umbrella sleeve is probably not a good idea either, if you slip with the umbrella and tear the liner, also no good.
I have seen numerable examples of tanning shelves in vinyl pools so I know they are an option. What I have not seen are umbrella sleeves nor bubblers in them. I can easily envision potential issues with the installation of both. I too have wondered about putting chairs in the pool on the vinyl.