The other answers seem to work so I'm not sure what's with the downvotes. I think the main point is that ob nicht doch is not an idiom and can be translated word for word. ob = "whether", referring to Zweifel, "doubts" in the previous clause. Remove that bit and switch to indicative to get Das Projekt werde nicht doch zu einem schlechten Ausgang führen. doch here is flavor particle/modal adverb/whatever meaning something like "contrary to expectation", "anyway", or, since we're in future tense here, "after all". It can be dropped without breaking the grammar to get Das Projekt werde nicht zu einem schlechten Ausgang führen. This is pretty straightforward.
I think the real difficulty here is that there are quite a few words with negative meaning (leichte, Zweifel, doch, nicht, schlecht) and this makes the sentence awkward and the meaning hard to grasp on the first hearing.