Mount /system/app/ using adb (non rooted phone)
Not from within Android, no. Only root can mount or remount filesystems, including /system.

There is another way, which is to go outside of Android completely by making the change you want from the recovery. Since the recovery doesn't use Android's permissions system, it can let you mount whatever filesystems you like, however you like. But if you're going to install a custom recovery to let you do this, you might as well root the phone anyway.