As others have noted, the HoI doctrine trees are fantasies. (Though HoI 4 is at least better on this than HoI 1 and 2 were.) The doctrines the various warring powers used grew out of the histories, perceived needs, geographies, material capabilities and practice. Germany in OTL did well early in the war due to a combination of the historically aggressive Prussian approach to war (which is perfectly sensible for a land power in the middle of a continent), the perceived needs of the Nazi party (who had an expand or die outlook), having temperate European geography and a head start of several months in figuring out how all the new toys worked out on the battlefield.
It all conspired to create a brief historical window where "blitz" tactics looked really good. But as the war continued, the ideas of the French, British and Soviet thinkers would prove more correct that Guderian's ideas. And there's no doubt that if Germany had the material means, it would have developed their doctrine in similar ways to their opponents, since Guderian was hardly the only German officer who could think about what doctrine should look like and the Germans were as capable from learning from experience as their enemies. And the officers who commanded in the late war took different approaches, though still approaches rooted in the officer corps' historic culture.
So if we look at the SA... Well, for a start they aren't an army when Hitler disposes of them. So if they become an army, where do they get their battlefield officers from? As such, if the SA won and became the core of the German army, it may be an SA dominated by officers who have been nurtured in the Prussian officer culture, and thus are going to have the same eagerness to emphasize attack and ignore logistics. If this German SA army goes through the same steps of Rhinland, Anschluss, Sudetenland, Bohemia then Poland, just like the OTL German army they'll have the same first-learner advantage that meant that the Germans were just better at modern war than any enemy they faced until they'd beaten equal lessons into the British and Soviets.
Possibly Hitler opting to build his army around the SA will slow him down, however. The SA being the core of the army is a really big shake-up and it's hard to see that NOT meaning that Germany is some months behind their OTL curve... That could very well mean Germany ends up being unable to conquer Poland, as a few more months to arm up means the French, British and Poles are much stronger vis-a-vis Germany. If Germany somehow did manage to scrape through and beat Poland, they could easily stall against France. If they do pull through, they may not feel they can beat the Soviets, or if they do think they can, a few months delay could mean they face a far more equal Red Army.
In other words, I don't think a German army built on the SA would be THAT different from their OTL army, since they are still drawing on the same Germany, but the delay of breaking up the professional army and reshaping the Nazi Party's thug militia into the core of a serious army could SERIOUSLY change things. And most likely not for the better if you are a German.
fasquardon