There are many factors involved here. It is not as simple as saying yes or no. Do you mean Chinese Men? Or do you mean western men? Honestly, in my personal opinion, asking a girl on a date that is base on drinking is not the sign of a quality man. Maybe he is a good man, but I think it is much more classy to ask a woman to dinner or some other activity. Some of these men may have good intentions, but to be completely blunt, some of these men may be more interested in sex than knowing you for who you are. My advice for good Chinese girls is that men who invite you to dinner or another activity are going to be better men in general. But this rule is not absolute at all.

As a woman I would be very careful of my own safety in this situation.

I mean go to the bar or somewhere he will buy you a drink.

What do you mean "will go with him"? To go where? :) Well... anyway - not.