I have heard of beer cocktails, where you mix 2 various types of beer to create a unique flavor. I dont see why you couldnt think outside the box and instead of mixing 2 beers mix beer and a monster energy drink. Worst case scenario, it sucks and you let us know so we dont try.
I say start small, dont potentially ruin a full batch of beer. Use two secondary fermenters, use something like a small 1 gallon wine jug as a secondary and mix your beer and monster in there. That way if it doesnt turn out the way you thought, you only lose a gallon and not the entire batch.