Yes, you can disable it forever [1]. Oh and there's actually a tiny "skip" on the nag screen in dull contrast, more user hostility. It's the concept I object to, though: If I pay for it, I should not be the product. And a privacy notice on something that's by definition supposed to be private.

1. Control Panel -> Info -> Device Analytics.

https://www.reddit.com/r/synology/comments/8mdioc/device_ana...