It wouldn't put a dent in the industry at all. We raise and kill cows for their meat, not their skins. Their skins are just a handy byproduct. Eliminating the cow-leather market won't change that at all; it might make beef slightly more expensive (I imagine most of the cost of leather is in the processing, not the raw hide), but that's not going to affect beef consumption.

If we mostly eliminate beef (in favor of artificially-grown beef, for instance, which might be a reality in 10-20 years), that'll make cowhides much, much more expensive, so people simply won't be getting leather car seats, leather coats, etc., except maybe for extremely high-end markets.