But the mods *are* loaded at that time, the server just uses another version or has additional mods which the client does not.
Example:
The server uses a mod pack v123.4. It contains modxy v11.23
The client uses an older version of that mod pack v123.3, containing modxy v.11.22
The user gets the mod rejection screen because of the newer version on the server.
If you now have users that don't have any clue what to do and what that means... you have a problem.
BUT if you can customize that screen, you could just replace the text with "An update is available. Please run the mod pack updater." And you're done.
It's a special scenario so I think if you can customize the text (cfg file for example), everyone would be happy with it.