Success really depends on how comprehensive things get. If say Goring gets loose and starts giving orders in just about any capacity there will be streetfighting and the army likely to step in. If its a smoothish coup my guess is the army will sit in barracks waiting for orders until its too late then find itself as voenspetsy.
I am thinking that even partial success might prevent WWII: Lets say that Rohm's coup only disbands the SS and reincorperates it into the SA. Hitler is placed under house arrest pending his "rehabilitation". Some key pro Hitler types are executed or killed while "resisting arrest" etc.
Rohm lacks the skill and the business backing to lead Germany. The now humiliated Hitler would make a poor super Fuhrer. The result, a right wing junta takes over Germany. Rohm has a place on it, Hitler does to, but more in a support role.
The junta contents itself with reclaiming the Ruhr, bringing the Sudentland into the Reich, and announces that Poland can avoid war if Gdansk / Danzig and German speaking Silesia are returned to Germany.