Not really.....
The Strum Abteilung ( NAZI BROWN SHIRTS ) started out long before the Nazi party took over control of the government. They started out around 1919. They were not a real government agency, instead they were a bunch of thugs who like to dress up in uniforms they designed themselves.
So while they had all sorts of weapons, they mostly had old military arms that they had hidden away or commercial guns they bought.
I think that the SA bought around 4,500 commercial PP pistols. So they are not seen all that often. But the ones I have seen are in good shape because they belonged to political hacks.
Hitler took power in 1933 and by 1934 all the SA leaders were dead.
The SA was then down-sized to the point of being irrelevant .
However they did continue as an organization up into the first part of WWII.
Two SA marked PPs that I have seen serial number to 1938 as a manufacture date. So somebody was still ordering them.
There should be a crown type proof mark on the right side of the slide under the ejection port. There should be another proof mark on the chamber area of the barrel.
I just looked at one yesterday that was in slightly worse shape than the one in your photos. It went for a touch more than $2,000.
They are often faked. Ones with capture papers can bring $3,000 to $4,000