Yes, you can use overlays and textures in this app on your mobile phone! No need for the full desktop version of photoshop!
UPDATE...
Unfortunately, Adobe has now removed this free app. Probably because it was being used so much and wasn't making them any money! If you downloaded it before it was removed, you can still use it! Yay!
Below is a great video tutorial link on how to use and add overlays in the photoshop mix app, for mobile.