I'm pretty sure you have to be specific with the dates on the permit, but it can't hurt to add that as a note. We haven't had to apply for one since 2006, and it might have changed. Our last hike in 2007 was a luxury trip. The day those dates opened up to book Phantom Ranch, we called and while my BF was on the phone, the computers all went down - he was able to book whatever he wanted and everyone else was locked out. So, we did a r2r2r staying at the cabins down at Phantom Ranch. Felt like rockstars.
For 3 days, I get to part of a thousand other journeys.