Mount /system/app/ using adb (non rooted phone) Is it possible to mount /system/app/ or to push an apk file to /system/app/ using adb on a non rooted phone? I am trying to use adb push to push an apk file to the aforementioned directory but it keeps telling me Read-only file system. Is there any other routes to take to try to push the apk file to my phone without rooting it?
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.