Leaving aside the anti-tank use of rockets and only considering the anti-aircraft aspect, introducing these rockets in 1942 has little or no effect for lack of suitable targets, i.e. large formations of daylight bombers.
Introducing them in 1943 will have nearly no effect, either, in the area that is not covered by Allied escort fighters. We know from actual history that the USAAF attempted daylight unescorted bombing missions in this area - and gave these up relatively quickly, after facing enemy fighters without rockets. This tells us that the rockets would let the German reach the same level of slaughter in a shorter time - and the USAAF decision makers would react in the same way, i.e. they'll withdraw and reconsider.
What remains is 1944, and, in 1943, the area where Allied fighters could escort the bombers.
Now, in order to judge the effects in this space/time framework, we should not, I believe, consider the single rocket. As others have mentioned, our concept of its effectiveness actually depends upon a salvo of rockets. And, I will add, the weapon platform also counts. We mostly assess these rockets' performance on them being fired from a Me 262.
But that aircraft isn't ready. So, will its forced replacement provide the same salvo volume, and the same balance of effectiveness vs. not only the enemy bombers but also the enemy fighters? I suspect the answer is no.
The piston-engined fighters available would probably carry 12, not 24 rockets; and their speed would never compare to the Me 262's. They would achieve some significant success initially, by surprise, and then they would cause a bit more losses than historically. However, the Allied response would be by means of their escort fighters, by changing their engagement tactics. As always, change brings about change.
A final, boring issue is what the Germans are not producing, if they mass produce the Orkan. Are they getting less Panzerfäuste? or what?