How does degoogling affect battery?
You can run Google free device, however you really have to know what you are doing.
Removing Google apps and services from an existing device isn't a recommended way. You may run into serious problems. The common way to get a Google free device is installing a custom ROM without Google apps (for license reasons most custom ROMS don't include Google services/apps).

If you disable GSF apps will loose the push notification service (if they still run at all). For a large number of apps GSF is a requirement.

Some apps have an alternative custom push system implemented but now every app has to run it's own background service. For example signal has such a service but the authors warn that it causes "reduced reliability or performance" and as every app has to open an own connection to listen for messages the overall power consumption increases.