Short answer: no. You can only mine with COIN while the app is open.
Our developers are looking into potential features that will allow you to mine with the app closed in the future, but there are many things that currently block us from doing so. The app currently cannot "mine in the background", due to restrictions about background battery usage that are placed on apps by both Apple's App Store and Google's Play Store. Should these restrictions be lifted, we'll definitely look into some sort of background mining capability, but for now, you can simply use the "Auto Collect" button.
Read this article for instructions on how to turn that feature on!