It's not tied to startup; there's a record of when this was last checked, and it gets rechecked if it wasn't within the last 24 hours. So that's likely to happen at startup (with probability related to how long Firefox wasn't open), but will happen while running as well.
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I believe the addons will disable themselves even if you disconnect from the network. Most likely workaround is bumping the app.update.lastUpdateTime.xpi-signature-verification preference to a timestamp in the *recent* (minutes) past while Firefox is *not* running. Untested.

May 4, 2019 · 8:01 AM UTC

1