Interest in implementing SIP push notification


Thats correct. Both have their pros and cons but UDP is unreliable when routing or tunnels are in place because UDP fragmentation is unable to work through stateless firewalls (missing header in fragments).
Connecting mobile endpoints should alwas use TLS for security or at least TCP to be reliable. UDP is perfectly fine for server2server (for example Asterisk <-> Kamailio). Sound quality has nothing to do with SIP signaling over UDP.