There is integration. I don't know what it is these days but it used to be mostly carriers adjusting TCP timeouts on their NAT boxes.

The issue is that a long lived TCP connection consumes some valuable RAM and a port number on a valuable IP address. It costs carriers something for push notifications to work, so, they tend to aggressively close long lived TCP connections that aren't going to recognised push datacenters.

For that to work you need business relationships with the carriers of course, stable IP addresses, and enough users of your push service for it to be worthwhile.

IPv6 would fix it by eliminating IP scarcity and CGNAT, but most mobile networks aren't provisioning handsets with IPv6 addresses.

The second page, on the right, the last bullet point, suggests such deep integration:

https://web.archive.org/web/20170708204409/www2015.wwwconfer...

Whether FCM uses these technologies, I don't know. I lack the hardware to easily inspect the mobile radio traffic on the necessary level (the best would be a DIY stingray based on one or two OsmocomBB-capable GSM phones, maybe combined with a Faraday cage to place one of them into, together with the smartphone.

The irony is, FCM is a modified XMPP