It will kind of. Law enforcement does not have unlimited resources, and its limited resources have to be prioritized based on the severity of the infringement. Lack of an "impressum" by itself would be quite tame unless there has been some other crime committed (or at the very least a credible tip or complaint) that would justify law enforcement looking into it in the first place.

Furthermore, when it comes to the lack of "impressum", merely determining whether the law has been broken would be difficult with proper anonymity. Let's say he's based in Germany but anonymously purchases hosting in the US or another country and never discloses his German residency on the website - in this case it's impossible from the outside to even determine whether he is actually breaking this law, removing the probable cause for an investigation in the first place. As far as I'm aware, Germany does not - and wouldn't have the resources anyway - to thoroughly investigate every foreign-hosted website to determine whether its owner is actually based in Germany and is thus breaking the law by not publishing an "impressum".