A week long backpacking trip sounds like 1) a ton of fun 2) a fantastic way to spend a week 3) a great thing to talk about during med school interviews.
If I were in your shoes, I'd submit in June, work on secondaries over the summer (either ones you've officially received or writing about that school's prompts as found on SDN), take the trip, and resume apps later.
The schools probably won't need to communicate with her much except to perhaps schedule an interview, assuming she has her ducks in a row enough that she could feasibly get interviews in August (I, for example, wasn't complete anywhere until September because of the way my school did committee letters). If she'd be skipping a trip so she could check her email to schedule an interview, why not give mom and pop the info to check her email, and let them schedule an interview should one come in? Sure would be a bummer to forgo an exciting adventure so you can sit at home and refresh an inbox.
Heck, isn't that what vacation responders are for?!