Unlikely. I suspect this will be a rubber stamp mill just like FISA in the United States.

That comparison doesn't make sense. FISC can only be a rubber stamp because only the US government can bring a case before the court. Any rando can sue German ISPs for not fulfilling their DNS blocking duties under copyright law, but certainly not just any rando can get their DNS blocking request rubberstamped.

The policy change also doesn't create a new court. The CUII is a voluntary cooperation whose members exchange information about sites they think they're required to block and agree to all block them simultaneously. Because this structurally looks like an illegal cartel, there used to be a review step by the Federal Network Agency Bundesnetzagentur to make sure that no illegal cartel things were going on.

The Bundesnetzagentur felt that this wasn't really part of their core duties, especially considering that there was a perfectly fine court system ready to use, so they asked the CUII to find another way of not looking like an illegal cartel.

Now the CUII will wait for one of their ISP members to get sued, in regular civil court, and if the ISP is ordered to perform a block, the CUII will put it on their list and the other ISPs will follow suit without having to redo the legal proceedings for each of them.

This change might very well end up increasing the number sites that get blocked, not due to rubberstamping, but because losing a civil suit is less risky than accidentally doing illegal cartel stuff and incurring a correspondingly large fine.