About your question: I don't think it would have major effect even if germans were able to largely replace older desings (full replacement would be obviously impossible, even in peace time such changes take time, during full scale war there's not even a question about it).
Considering german situation in late 43, 44 and 45 better infantry weapons were probably one of the least pressing problems of the time. After the disasters of Stalingrad and Kursk third reich simply did not have enough manpower to employ it's infantry divisions in anything more than trying to seal gaps in crumbling frontlines.
One of the biggest advantages of the modern assault rifle design is it's flexibiity, which allows for using it in various battlefield situations. The problem here is that germans were mostly pressed into one particular type - defence agains overwhelming enemy numbers, a situation in which sturmgewher flexibility could not be fully employed, thus it's potential impact would be probably lower than expected.
Okay that's my opinion on the subject matter, looking forward to discuss it more.