The warhead was really too small to accomplish that. From everything I've read on it, they intended it to shoot down planes but had serious doubts about its accuracy and the lack of a proximity fuze to do it. You needed to only get close to shoot down a plane. That was how most SAM's through at least the 60's worked.
What surprises me about the German SAM program is:
First, they didn't pursue a ramjet missile. This would have given them a SAM with greater range and reliability than a straight rocket, solid or liquid fuel.
They made little or no attempt to improve solid fuels.
They failed to consider a much larger proximity fuze using a small on board radar given the room their SAM's had internally. Command detonation was explored at least some.
They didn't aggressively try and improve their electronics technology.
Of their SAM designs, only Enzian might have worked to break up a bomber box. With a 500 kg warhead it had the possibility. Of course, any SAM in service really needed to be able to intercept RAF bombers at night flying in a stream too. Again, the only real option was being able to target and engage single bombers.