It would be great if you could guarantee to release every 60 days a new version.
But can you?
If not, users would be annoyed if the software would say “I’m outdated” but on the server is no newer version.
And what about hot fixes for critical bugs?
Have the (not informed) users to use a not patched version up to 59 days?
IMHO the risk of tracking is less critical if you would realize it a way as I said before.
More less risky then use a not patched software.
And the thing about centralizing:
I download the software also centralized from your GitHub account
And as I said before. You could add a option to switch off checking for updates.
If you like to be absolutely sure the user will not loose the control over this, you could ask on first start (maybe after every update if you like) “check for updates automatically?” [Yes]. [No].
And a check mark “never ask again” to store my choice for ever.