Ulfric very much does not believe the Empire has what it takes to fight the Dominion. And that belief is, as I've been arguing for what feels like half a thread now, not baseless.
Look at the final dialogue with Tullius in the "Stormcloak victory" scenario. It's one of very few instances in Skyrim where the writing actually moves me:
I think this little scene shows both sides at their best. Neither Tullius nor Ulfric is blind, but they're both convinced of their own rightness. Ulfric says "The Empire... never surrendered" - which implies that the Empire stopped being the Empire when it signed the Concordat. The Markarth Incident was Ulfric giving the Empire a chance to redeem itself, and it blew it - as it's blown every opportunity since to actually stand up to its new overlords.Originally Posted by Battle for Solitude
I don't really see how you can expect Ulfric to put any faith in the Empire, after that.