The ringback you hear (that's the "ringing" tone you're talking about) is generated by your carrier and sent back to you when it gets a notification from the carrier of the person you called that the call went through to ring that phone. (It's actually central office to central office.) You don't hear the actual ringing. (If you did,it would be more of a "burring" sound on a landline - it's 20 Hz on a landline and a digital signal on a cellphone [and all you'd hear would be a few clicks - once].)
WhatsApp is pure mobile data (or WiFi), it has nothing to do with the telephone system. If the person you sent the message to has no mobile data, or has mobile data turned off and is out of range of his WiFi router, he won't get the message, but he'll still get phone calls.
If you used the normal SMS texting app, it would go through as long as he can get phone calls.