Is it viable for running? Or does it have any differences that might make it a disappointment to run?

I don't think it's even allowed to speedrun in the Game and Watch version. It has secret cheats. For example, in the title screen, if you hold down A for 5 seconds, you'll start the game with infinite lives.

Got it

I think it would be okay at best, but there are a few reasons why it isn't really done. Honestly I think it would be neat as a category extension, but it's a pain to record and I'd bet most people who have the G&W version can already play the game in a different form. I'm not an expert on how that all works for verification purposes, but it would be pretty easy to see that you weren't using any of the cheats that the version allows. Since it's not listed as an official system to use, I'd steer clear of it for now if you have any other option.

The closest you can get to use it is for a meme category or if you want to make your own speedrunning site for it (and other meme categories like beat 4-1), but that would kinda be a hassle because you'd have to be good with JavaScript. Either way I actually kinda like the idea of a different site (but again, making a website is no easy task).

You could make a google sheets leaderboard

Yeah I guess you could, but that would be pretty clanky imo