Having said that, you are probably correct in thinking that the majority of players would want a card game with either minimal story (i.e. text to read) or none at all, since that is just what players are used to and have come to expect from card games.
I think your idea about splitting the game into a card game component and a VN component may have merit, but I guess whether it is feasible would depend on how difficult or time consuming it would be to implement. Some things to consider from my perspective... Using the "card game" as the base with the VN part as DLC runs the risk of upsetting/alienating the people that are purely interested in the VN part. Also considering how people tend to react these days, if you were to sell the game as a whole with the options of "Battle mode", "VN mode" or "Battle + VN mode" within the game itself, there is a chance that the people only interested in e.g. the card game portion would complain about paying for the VN as well (when they have no intention of playing the VN part). So like you mentioned, having a free demo base with the card game and the VN as separate DLC may be the best option if you still want to implement both.
But in the end you need to do what's best for you and what you believe will sell
On another note, you can sign me up as a "beta reader" if you want
