Can a 3 sim card (UK) work on a verizon phone (US)

[rymannss]

I have a sim card from 3 in the UK and I'm in the US I just got a note 8 and everything seems to be working okay. I don't want to go home and it not work. I have my UK number on this phone and can send messages and calls. The data seems slow sometimes but that might be because it's a UK sim card and I'm so far away. (It says I'm connected to T-Mobile). It comes up with the "this sim card is not from verizon wireless" but when I called they said it's unlocked as they all come unlocked now. Will everything in the UK work as a phone should and will the phone connect to it's own network when I'm there

Thanks.