If you're only concerned about chrome / android, and want to throw in desktop notifications for even Windows and Linux, you should be ok with just using javascript Notifications API. One good thing about FCM though is it throws in some additional iOS notification support, but last I checked you still had to have a native iOS application to actually send the push notifications to.
Even people on iOS running Chrome can't get Chrome notifications. If you're going to make a notification extension, it would be best to support them in some way.
