The distance between the low E (depressed at 24th fret) and the bridge pickup is 2/16ths of an inch
That's only an 1/8 inch... Way too close. You'll have output issues, possible string buzz, maybe even magnetic issues that sound like bad tuning or intonation. Anywhere between 3/8 and 5/16 is fine depending on the pickup and the output you're looking for. I keep my JB's at 3/8, and they SHRED. You never want to have them too far away either, because of the same problems. Here are a couple of good, helpful articles.
http://www.projectguitar.com/tut/aph.htm
http://www.gibson.com/en-us/Lifestyle/Features/Tone Tips_ Pickup Heights/