At least on the iPhone, the tripit app itself requires an internet connection to get your itineraries. Right? So, you're out of luck there.

But, you can do a TripIt ical Feed and that will load into the iPhone's Calendar App. That data stays in your phone whether offline or online. So, you can have "offline" access to your itinerary via that method./ Admittedly, if you updated your itinerary online via the web or by sending additional flight/car/hotel/etc. info to [email protected] that new info would not download to your iphone Calendar App b/c the iPhone is not connected to the internet while you're abroad.
It's been a while since I set it up, but I think I feed my iCal feed into Google Calendar and then get my google calendar via the iPhone Calendar app. I am sure TripIt has instructions... Yup .... https://www.tripit.com/uhp/calendarInfo (NB I don't know if the "Apple iPhone and iCal" instructions will work if the iPhone is offline, that's why I use the Tripit->Google Calendar->iphone method at the start of the help article)

I usually go with the method discussed in the paragraph above as well as a printed copy. Frankly, while I have the tripit app on my iPhone, I've hardly every used it.