not only apply, but make an exceptional grade as he will be competing against tens of thousands of other kids in NYC who are trying to get into the specialized high school program. It is not as easy as "applying to take the specialized high school test" - dont be fooled by the brief answer below. High school admissions in NYC is EXTREMELY TEDIOUS and you have NO CONTROL (unless you go the private route) over where your child is "placed" - the ONLY option you get (again, if you do not go the private route), is if your child is placed in both a good high school AND a specialized high school.
The EXAM itself is LONG and tedious. I highly recommend having your son work with a private tutor so he can learn skills to cope with his ADHD while sitting in a room full of other student (hundreds, if not more) at a time, remaining still and quiet (or he will be removed from the exam) and being timed on each portion of the test.
I hope you have plenty of time to work on this, as the process starts immediately in 8th grade.
Best of luck to you.
And, please, do not get your advice from the internet - even what I am telling you is from our experience this past fall (2012) - this is a very stressful process and mirrors college applications, but at a much younger age for the kids and they are not used to dealing with testing and waiting six months to find out where they are placed. (the exam was in October and we find out next month, in late March)...