I actually already know the answer the this question (now), but I wanted to make the answer explicitly available for others.
In short, if you boil them overnight (and the volume does not change), you will get very smeared bands and render them useless for Western Blotting. I've attached some photos so you can get a side-by-side comparison of what you'd want and what you'd get.
I left them to boil for ~15 hours at 96 degrees Celsius.
Image one is the boiled blot for Actin and y-H2AX (membrane cut), while the 2nd and 3rd are the correct results for actin and y-H2AX, respectively.