In a word, no. I don't know what your vet was thinking

.
First off, if there is a lot of damage, she may lose a quarter. It literally sloughs off - horrible to see (and smell!) but it isn't life-threatening (although make sure you keep it protected from flystrike.) It would of course mean she shouldn't breed again.
Hopefully, as you've caught it early, that won't happen and she won't totally lose a quarter. However the next level of damage would be if it leaves lumps, bumps, hardenings in the udder. You should check all your ewes 'above (teeth) and below (udder)' before tupping anyway; anything with hardenings or lumps is suspect and may not be suitable to breed from. (Whether or not you know them to have had mastitis.) Experience helps you decide which should be ok and which must go - if, when the time comes, this ewe has anything other than a 100% soft, pliable udder, then personally I would at that point cull her.
She may make an apparently full recovery, nothing untoward to feel at pre-tupping checks - but then struggle to produce enough milk for two if required to do so. In my experience, this is a very likely outcome - sorry.

However, you've caught it good and early, and are treating it aggressively (you
are stripping the affected quarter out at least twice a day, aren't you?!), so if any sheep can make a full recovery then she has a good chance of being that sheep.
