As a "stupid thought experiment" that's a fun thing to consider. (Somewhere I've got a proof-of-concept perl script that steganographically embeds PGP encrypted messages into an image of the FBI logo and posts them to Twitter. I would not ever actually use it in anger... I still have the private key for all my test/gag posts, just in case I ever need them...)

But if you're _actually_ crossing a border into a country where there's internet access, why would you risk carrying any data that you wouldn't put on a postcard across that border? If you need it, download it after you've got there.