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Can't say anything about influencing you embouchure since I've had one since before I touched an instrument. I guess it'll feel strange the first few weeks because they never really can make a 100% exact copy and your mouh is extremely sensitive to tiny changes.
I can say mine's still there after 25 years, and I've played french horn (used to professionaly) with quite a lot of pressure for 20 of those years.

I have had a crown on one of my front teeth since before I started playing tuba, so I can't address the change to embouchure, but I have never had any problems with it, and I've had it more than 30 years. As long as they do a good job matching your existing teeth it shouldn't be a problem.

One of my lower incisors broke diagonally about 8 years ago (2 days before a concert), leaving "nice" sharp edges for the tongue and inner lip. My dentist rounded-off the sharp edges so I could play the concert, and made & installed the crown later. It's been no problem at all (less than the original, actually, because it's aligned properly -- the original was twisted a bit).

I have crowned incisors and it's not a problem. I only have a few of my front teeth left and I was amazed how little I had to change about my playing when I lost most of my teeth and wore removable dentures. I won't make a public show of it, but by removing my bottom plate, my lower notes are so much easier!

I have crowns on two front teeth...no problem. However since I started up tuba again after the crowning (and after a lapse of 50 years since I previously played tuba), I can't remember how I sounded with the original choppers!

I have crowns on the 4 upper front teeth. No problems whatsoever.

i have a crown on my upper teeth.
i can't say how it affects my playing because i had the crown "installed" years before playing tuba.

here i was thinking i was the only one.