The VN probably needs to be free of H-scenes for that to work. Meaning no SR. With all the comedic rape in that game, I'd think western audiences wouldn't like it too much.
It's a tricky question. Most of the VNs with gameplay that I know have some sort of H element, and their gameplay isn't fun to watch at all. I supposed it would also need to be translated, which narrows things down even further...
Honestly, I can't see it working. The closest you can get is probably some other games with dating sim elements, like persona (which still wouldn't be enough for an E-sport), but actual VNs are tricky.
A VN stream can be successful, but it'd probably be one of a VN which doesn't have any gameplay. Well, Dangan Ronpa could work out, but not as an E-sport- the gameplay is secondary and way too easy to be taken seriously.
This might just be an issue of me having poor memory, though. I'll look out some VNs, maybe there is something which could work out.
From tld ones, Daibanchou may work out- who you talk to and all the character events have some importance in their combat performance, and the gameplay is a really major element- not too boring either. It's an alicesoft game, though- so it's full of H-scenes, just like rance.