Absolutely. And if the Otterbox you are using has a "textured side", the grip will hold even tighter. The mount has a WIDE spread set of side grips that are spring-loaded such that once you place the phone (in Otterbox) against the back of the device, it will SNAP tight on the phone and not let it go until you squeeze the two "release levers" when you want the phone back out of the holder.
Any mobile phone will fit. The minor additional width a case adds is still no problem.