Even in that case, the catholic south would go for a reform not for a breakaway.
I try another way: How about a revolution lead by the SPD and other moderate elements? Topple the Kaiser! Go full Republic!
Possible, I suppose, but I doubt it would lead to a breakup (except maybe in the case of border areas that aren't ethnically German). To be successful, a revolution hasd to succeed in Prussia. As long as Prussia is in the opposing camp, no other state could break away as a republic. But onxce the revolution is successful in Prussia, no other state could withstand it. And the erlected governments of all German states would vote to stay in Germany, so that would just produce a German Republic.
Maybe the new republican government would allow plebiscites (or simply give back/release) North Schleswig, the Metz region, even all of Alsace-Lorraine, and the Polish-speaking areas of Prussia, but I doubt it.
Edit: even if they did, what would Posen do?
"Hey, Polish brothers, you're free now!"
(looks over shoulder at Russia) "Can we stay? It's dangerous out there."
"You're independent and free! Be your own country!"
"Ummm.... Austria-Hungary? Can we join you? Please???"