Are (servant) bosses vulnerable to death?

Generally enemy servants have a death rate if 0.1% that is to say if you use a 100% death rate NP it will take 1000 attempts before it works on average. So technically yes but in reality not so much.

It is possible to instant death a servant. I once instant death Ibaraki Douji on the Rashomon event

As others have said, servant bosses have a non-zero death rate, but realistically you can't assume it'll work. If you just need to beat ozy, I recommend bringing a single-target assassin (Jack, Shiki, Emiya...) or berserker (Kintoki, Herc...). Raikou also works even though she has an AoE NP, because the hits hard anyway.

If you are talking about the one in Camelot where you have to fight him 3 times, Kintoki rider is a good pick plus he is a welfare servant, I know he is a rider and does not have 2x damage, but at least he won't get kill by the caster in the same wave like assassins, and his NP charges up super fast. I usually put an assassin in the back and have kintoki finish off the casters first. Then just switch the assassin out.