Is it ever ok for a teacher to go out for a drink with an (adult student?)?

I would say no. If they are both male and the same age or the student is older it’s a maybe. 

if you're talking about university faculty, many often go out with students for drinks- in groups. Our Creative Writing faculty and students regularly do drinks in the afternoon, sometimes with readings of things the students have written. Going out alone is trickier- usually not against policies, but dangerous for the teacher. Other people may see it and misinterpret the relationship. While it is not unknown for professors and students to fall in love and get married, it is also not unknown for students who feel rejected to file complaints of sexual harassment. It's just better to avoid the whole issue. 

Not okay, ever. The teacher, whether it's in person or online, is in a position of authority over that student and this blurs the line, opening the professor to bias because he or she likes the student. In an attempt to avoid bias, they might even grade the student harder, which is another form of bias.

If you and your teacher want to have drinks, drop the class.

Many colleges and universities will fire or censure a teacher who violates such a basic ethics clause that's in most teaching contracts.