Sealing won’t keep the paper towel shreds from getting rubbed off into the crevices, or even the grease splats and spaghetti sauce splats from getting into the crevices. It will give you a bit of time to get out the scrub brush and ammonia and scrub off the offender though.

Better do a mock-up and see if you can live with this in real life. Visually and functionally.

I would not choose this as a backsplash material, esp behind your stove. It's just not a practical choice and one you will probably regret. Can you incorporate that rustic look in other ways? Love Muskoka btw...

How are you going to clean that? It should be ceramic tile.

What does the manufacturer say? What kind of stone is it? It looks sort of sandstoneish, and that might suck up grease.

I'd seal it. But that will affect its appearance a little bit so you should probably do a sample first and make sure it still matches. While you're testing the sealer, test food stain resistance too.