YES! One of the biggest benefits of Readly is that you can read anywhere, anytime.
You can download and save anything between 10-500 downloads locally on your device, providing you have enough memory on your device. To view the downloaded issues you will need to open the "My Content" tab and then scroll down to 'Downloaded'. The little yellow circle (around the plus icon) next to the cover shows how much of the magazine is downloaded (and then can be read without an Internet connection).
Tip: If you know in advance that you will be without Internet access for a while, download as many issues as you want in advance.