I would advice caution with that approach. Not only could Linux by itself be "suspicious", a clean OS without any data surely is. Once they have a justification for a deeper search they will find out about the live OS and you will be treated like a terrorist.

A better approach would be to backup your OS and make it available online over SSH/VPN for example. Then install windows or any other default OS on all devices with some amount of believable but not too personal data. Once you are over the boarder wipe all devices and download your real OS and data over the internet to your devices.