Can do. But shouldn't?
It is possible, in the short term and up to a point. I think in any case "public key" encryption, yes I know that's something else, in practice uses a non-public-key encryption whose key is encrypted with the public key, because actually using the public key for all communications is very very slow.
So, what WhatsApp could have - and, as a selling point and mission statement, does not have - is the session key encrypted with the users' public keys, and then the same key encrypted with the government's super encryption public key, once for each government that demands the right to view all the private WhatsApp messages.
Of course, whenever any of the governments' special keys is broken or leaked or whatever, then all previous messages become readable by anybody. And one or all of the special keys has to be replaced
But, what you did is, you then sent your messages over SnapChat, so they have been deleted!
I'm not an encryption professional, so I may have some of the details wonky.
I wonder what Amber Rudd thinks would have been different if the government was immediately aware that one religious person in the Westminster area had just sent a message saying "Geronimo!"
These people say "God is great!" at least five times a day anyway. That makes it seem to me that someone suffers from insecurity, in a sense besides "reading secret messages" or "terrorist attack".
Anyway, here in Glasgow much the same thing happens when someone is drunk - although, to be fair, there is a fuss about it afterwards, too.