If you can handle the drinking and it doesn't make you sick yourself, you can date an alcoholic. If you start to wish she would quit drinking or try to control her drinking in any way, you are setting yourself up for a big problem.
Ask yourself how comfortable you are watching someone slowly kill herself.( I'm not being sarcastic.)
I've got a friend who got sober himself but is still married to an active alcoholic. They have an oddly harmonious life. He is really dedicated to his own sobriety and completely detached from her drinking. I feel like this is very rare though.