To me, it looks like it could work much like attack copters for the US Army if WW3 had happened. Breaking up enemy armor formation in counter attacks, breaking up strong points while attacking, and breaking up artillery parks. I am working under the assumption that these units would respond quicker to army needs than the Stuka units. I sort of envision these units being used much like one uses artillery batteries from division/corp being assigned to support the focal point of the attack. If I remember the term correct for divisional artillery, it is the Primary/General Support mission. As to effects, I think it would vary by year.
1941: Probably not a huge impact the first few weeks of the war. Things just went so well. But these planes are capable of very rough strip operations, so they could keep up with the Panzers. There are battles in Army Group Center where Panzer units were temporarily cut off. These planes could help restore the connections between the advanced units. If reduces by a day or two these pauses, then some opportunities can open up. For Army Group North, these might be enough to break through some of the defenses that slowed down its one Panzer army. Maybe this unit can move fast enough that Leningrad falls or at least enough more is taken that it can be starved out in the first winter.
You also get stories of 1-4 heavy Soviet tanks holding up a Panzer division for a day. With rapid response from the Hs 123, these events should not be happening. I don't know if this really was a major issue or just makes a good story. I think you can take a lot of battles where Russian heavies slowed down an attack, and assume that the Germans break up this formation within a few hours.