xxx You can disable it for sure. Doesn't break things.
The bundled Gallery app provides functionality by responding to various intents that other apps may call. The Compatibility Test Suite includes checks that these intents are handled. Every stock Android OS will handle them.
Most alternative Gallery apps lack the ability to handle all these intents so it may be you have other apps that have broken functionality if you disable the bundled Gallery.
Not sure I have ever seen an app send an intent to view https content in Gallery. That may well be the only reason Gallery has network permission. But there is some chance that some 3rd party app relies upon that for some critical functionality.
It is possible to look at the manifest for an app to see details of all intents it can handle.