I'm not sure how to answer that question. Android Pay definitely has to have NFC. If you turned it off the logo would go away but it would not work.
Samsung Pay uses NFC for terminals that have that technology but it also uses a different type of technology to mimic a credit card swipe (I can't remember the acronym) on terminals that do not support NFC payments. So, I don't know if NFC has to be on for those type of payments to work or not and I don't know of any quick toggle for that that is separate from NFC.
One other thing to note, if you are using that type of payment it has to be on a machine that lets you swipe the card. If it's one where you put the whole card in then it won't work.