Yes, the "Sie" refers to the person(s) you are addressing to. "Sie" is used for the polite singular or plural.
If you are talking to friend you would use the collegial form: "Bitte, trinke (du) mehr Wein."
I would use the "du" just to emphasise the person you are talking to - or better his/her name. Especially if there are more people present to whom you could be talking.
(Or some more slang: "Komm, trink noch 'nen Schluck!" = "Come on, take another sip!")