Drinking and writing This may be a sensitive subject given the subject matter. 

But I have currently experiencing significant writers’ block when it comes to writing my statement of purpose and personal statement for graduate school applications. As part of my research (procrastination) on how to resolve this issue, I came across some material that suggested that a minor intake of alcohol would allow the process to flow more freely.

Not enough to inhibit writing, but enough such that the usual inhibitions are removed.

I wanted to confer the advice and wisdom from the academia community on this subject matter, the pros and cons, the potential ramifications of such an action. 

What are the effects/results of drinking and writing?
Massimo's comment reminded me of the old adage, "drink when you want to, not when you need to", and I think those are useful words to remember.

However, I also agree with what rnrstopstraffic said, and if you have no general problem with consuming alcohol, try it and see what happens.

I don't suggest going out with your friends, drinking 6 pints of beer and 3 shots of tequila before stumbling home at 2am and scribbling nonsense, however. One glass of wine or beer with dinner would, I expect, be enough to get the creative juices flowing (if alcohol is going to get them flowing at all). I also recommend that you wait until the following day to edit and submit.

I've personally never written academic work after drinking alcohol, but I have written fiction after doing so. For me, it definitely doesn't improve the quality of my writing, but it does help me put pen to paper (or fingers to keyboard) and just write. As Inkblot says, it's a lot easier to rewrite and edit when you have something on the page, even if it is total garbage.