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 select the 'Downloaded' section of the Readly app. The little yellow stripe under the cover shows how much of the magazine is downloaded (and thus can be read without 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. You can download several at the same time by clicking on the small cloud download icon under each cover.