It doesn't seem like it. I tried for awhile to move the needle on emoji domains, got nowhere....
What do you mean? As far as I know, all current browsers do support them.
Without converting to punycode?
There are no IDN domains "without punycode". If you mean the display, both Firefox and Chrome do show them as-is at least in some cases - but as far as I know do have policies show the punycode form in others to avoid phishing attacks.
Alright yeah that was what I was referring to. Are phishing attacks the only real thing holding back full support? I'm wondering if maybe a notification that the domain is an IDN similar to how they notify about bad https for anything they don't already fully show would do the trick. Seeing as how phishing is not currently a solved problem, would it really be that much worse if all IDN's displayed properly?