Earlier quoted context omitted.
The phrase "running continuously" makes it sound like they are doing something... but they aren't: they are blocked reading on a socket. The only time they would run is if they receive information, which is exactly when they would run anyway (as they got a notification). The difference in battery usage would essentially be down to subtle effects caused by the private memory of that process (which might be negligible)…
The main issue with what you're mentioning is usually the fact that only Apple and Google servers tend to be whitelisted on telco routers for long polling connections. Trying to keep long-running HTTP connections for everyone else tends to be extremely hard on battery life since telcos can kill of connections even as often as 2 - 5 minutes. Powering up the main core and radio so often will make your phone hardly last…
Especially in the EU where no favorable treatment is the default (so net neutrality) - as far as I know.