If you then attempt to connect to a server - either public or private - with incompatible or missing mods, an error will display telling you that you are missing required mods.
I haven't noticed any errors when testing myself between LAN devices (one modded, other vanilla), neither did random people who surprisingly managed to join me in public lobby.
Even if server/host uses LobbyCompatibility, clients without LobbyCompatibility may still join (and often get stuck in the infamous black screen limbo), so it doesn't really prevent the issues.
Conclusion: this mod is a "nice to have" UI feature that doesn't provide any actual guarantees.
I haven't noticed any errors when testing myself between LAN devices (one modded, other vanilla), neither did random people who surprisingly managed to join me in public lobby.
Even if server/host uses LobbyCompatibility, clients without LobbyCompatibility may still join (and often get stuck in the infamous black screen limbo), so it doesn't really prevent the issues.
Conclusion: this mod is a "nice to have" UI feature that doesn't provide any actual guarantees.