Almost but not exactly, any rational merchant would estimate how much they pay monthly in credit card fees and find a way to add that back to their revenue. For most practical cases, the business is started already after the existence of credit cards, so when modeling revenue in your business plan this should already be baked in and the prices you come up with already cover it.

So it doesn't mean they increase the price of every product by 3%. One guy might charge more just for coffee, another do some other thing. But any extra cost you put on a seller of anything, the rational seller will make that back in sales somehow.

A rational merchant would know that they are also incurring costs for handling cash, and depending on the size of the business that cost can in fact be higher than the cost of handling cards.

In fact, the low end of cash handling costs for a business will almost always be higher than the card fees alone, but of course there are other costs in managing card payments too, so it's not quite that clear cut.

In particular, that is what happens when costs are imposed industry wide, as with credit card fees.

If the cost is only being paid by one vendor then that vendor can't raise prices or else customers would patronize one that had lower costs and passed on the savings. But if every vendor has to pay 3% then prices are going up 3%, because then the competition has no cost advantage they can pass on and people only stay in business if they're making enough to justify not doing something else. (3% is more than the entire net margin in many industries.)

the seller just charges whatever it get can get away with. 3% only has an impact when margins are closer to that percentage