Yeah, I think that'd be cool. BTW, battles are a way of breaking up game play with "differences in kind" so that a player doesn't get bored because it's all the same all the time. You'll either need to make the game shorter or make another game play element to break things up a bit.
I tend to think more and more on this for my own projects, I have a few ideas for some myself, though usually they don't have battles because they focus on a different aspect, and are more "sim" in nature (Think Harvest Moon).
I think it depends largely on your intended audience if it works or not. I personally can't stand most VNs, which has more to do with the setting and bland premise than the style... there is a noticeable exception, Loren: The Amazon Princess I absolutely loved... but it did have battles (though that was not what I liked about it)
If you make a TRUE VN then you will probably get better feedback from a VN community, while there's some crossover between different communities I don't think there's as many people here interested in VNs over RPGs, not trying to discourage you but just letting you know of your audience