Comma anyway

A father comes home after a night out. A friend of his has been babysitting for him.

Father: Have you been drinking the wine I left out for you?

Guy driving: No.

Father: I don't think it goes well with babysitting, anyway. (...so it's probably for the best that you didn't drink it)

The thing written in parentheses is added to explain what he means with the sentence, it's not something he adds.

1) Is the third statement natural in the context?

2) Can it stand alone?

3) Is the comma before "anyway" correct?

4) If I didn't add the comma before "anyway" would it then sound like the father previously has said that it would go well with babysitting but now has changed his mind?

Thanks in advance.