Should you a girl a drink? Well, this depends on the situation, but as a first chat up line I would say no.
If you nervously go up and ask girls if they want drinks all night, you are going to waste a lot of money.
Many girls will talk to you for a while if you are funding their night out. Some girls will take the offered drink and just walk off. If you spend all night buying them drinks, are they into you or your money.
If you are going to buy a girl a drink, it should not be the first thing you ask her. Talking to her for a little bit will give you an idea of whether it is worth your time getting her a drink and whether you really want to talk to her anyway.
If you are getting desperate, you called always try this.
If the best opening line you have is buying girls a drink, then you need to work harder on your dating skills. There is a gamble buying someone a drink, but it is best to start off a conversation first so you know what you are betting on.