The short answer is no, unless you are in a specialty practice in a field where euthanasia is unlikely - say, dermatology - but even then you may encounter it.
The long version: Euthanasia is a wonderful gift we can give to our sick patients and their owners when the pet is suffering and cannot medically be helped any more. It is NEVER easy - it's not supposed to be easy. But it is often the right thing to do. Even when I'd been working in a practice for several years, euthanizing my own animal was one of the hardest things I had to do. He was just a kitten, but he had a horrible heart defect and when he went into acute heart failure, the meds just stopped working. It was so much kinder to put him to sleep than to watch him suffer while dying a "natural" death.
There is also a big difference between that, and working somewhere that does "convenience" euthanasias - say, the family can't keep their perfectly healthy, well-adjusted dog any more, so they want to put it to sleep instead of finding it a home. Or the cat is urinating on the rug and they don't want to go through diagnostic testing and behavior modification, they just want to euthanize. That is something you will encounter in general practice, because that's what some people want. I have never worked for a vet who will do it - my first practice had strict policies about euthanasia and not having to endure "that" kind made it much easier. Not that it still wasn't sad, and I never cried, because I did. But we were always doing what was best for the animal.