HTTPS over UDP is secure. This is because the security of HTTPS doesn't use any of the properties of TCP except that it is a transport layer. Just like UDP, TCP is easy to spoof and manipulate. TCP is only to make things more reliable, not more secure. With UDP, packets can be doubled, missed or sent in the wrong order. TLS is a means to fix these issues. TLS works on UDP instead of TCP. But then those issues would make the encryption more likely to break on one side, and the connection would fail.
If you start to add error correction and other features to higher protocols like TLS, you basically re-build TCP, which is bad as then you have to maintain (and build) your own TCP stack with all the problems this introduces.
The UDP connections you are observing are most likely not SPDY, as SPDY uses TCP for transport.