The effects would be relevant, especially in operation Barbarossa.
The German panzer arm fared very well in 1939-40 even with its PzIs and PzIIs, which is a monument to doctrine, tactics and combined-arms balance. Adding the PzIII to those campaigns doesn't change them a lot.
However, when we come to 1941, Germany has 20 Panzerdivisionen. In June, one is in Africa and two are refitting; 17 are immediately used for Barbarossa.
But they had, on average, just 192 tanks each. And those having more tanks than that, normally were the Czech-equipped divisions, with the Pz35(t) and Pz38(t).
So, assuming the Germans have just 400 PzIIIs more, they can either outfit two additional Panzerdivisionen, or significantly reinforce the existing ones. And the difference is likely to be felt.
Now, of course this assumes the Germans produce all the tanks they produced in OTL, and _on top of that_, some 400 PzIIIs more. That's unlikely. Steel, rubber, production lines, and money are what they are, and, as others have mentioned, the Germans are already rearming as fast as they can. Something has to be cut.