Most programs will give you deadlines weeks and weeks in advance. Just fill out the paperwork as you get it. They know people are travelling in May/early June, and I've never seen it be much of an issue. The only thing I'd say is to *communicate* with your program leadership, and that you should make sure you are somewhere you can get emails. I was in Israel in June before I started residency, and when I scheduled the trip I shot an email to the PD and coordinator letting them know that from June X to June Y I'd be out of town. Before I left, I took care of the paperwork for the program and for the VA. Then, I just made sure I had access to data or wifi every couple days to keep an eye on my email... and the only thing that came up was the VA wanted me fingerprinted for the umpteenth time. I called over VoIP, arranged it for when I came back, no big deal. OTOH, if I had been on safari somewhere and hadn't checked my email for 2 weeks? Might have been an issue...Also keep in mind that a lot of required time sensitive and likely to get your ass kicked or fired for being late stuff starts happening right after match day but is at a peak cresecendo in the weeks leading up to June.
Some of it will require original signatures on original paper and urine/clinic appointments at facilities locayed nationwide, meaning yes, your program 8 sates away could require you to go somewhere in your state the month of May for a piss test.
You will need to be available at any time after the match by phone/email within 24 hrs of your program for the most part.
Any deviation from that above statement you will need to make very clear in advance of your vacation after match or else.
Just assume that you are owned by the program for any whims after match day.