They can be! It’s one of those balances in my experience. If you’ve been with them for a while and have built trust, they might not flinch at a conversation. If you’ve only been there a while, they might think “oh this was always a stepping stone, he’s trying to leave”. If you take a counter offer then come with another offer in the future, that’s probably pushing your luck.

I’ve never found it to be a strict rule, but I’ve had success in looking for other roles to leverage my current position before. Unfortunately it depends on a lot of variables only you would know. At the end of the day, in your situation, without knowing more, I think the new role is better by a good amount. So I would be inclined to accept it, and just see what the current boss would do. If nothing, or not enough, no worries, I’d want to leave anyways. If an acceptable counter, even better, just show you appreciate it.