Absolutely yes!
eDirectory is mobile responsive and has a fluid layout that adapts to any screen and device used.
Although the standard of the platform is to be mobile responsive, some codes added in HTML editors and Custom Contents may not be, as they are HTML codes generated based on the users' input, and may cause a bit of layout break.
There is a handy work around for making images responsive, just follow the screenshot below:
You need to edit the html source of these widgets, and add class="img-responsive" inside the tags.