Having Public Consumption on my record to greatly affect my PhD applications?
I would do everything I can to prevent this going on my transcript. The first thing I would do is write a letter of apology to the cleaning crew for my misbehaviour. Do not approach the cleaners directly, but rather through their boss. Then I would contact the head of the MS program to explain what happened. While waiting for that meeting I would schedule a meeting with an alcohol counsellor so I could demonstrate I do not have a problem drinking. You may also want to enrol in a workplace sensitivity training course.

I cannot recall seeing an application with anything like this before. I don't think people would really hold it against you and you could explain it in your cover letter. That said graduate school admission is competitive.