It could. It's hard to say how the name was distorted, anything is possible. You should look for the nearest Catholic parishes in the neighborhood(s).
Anyway, many Poles looked for jobs in Germany especially Saxony in those days. A lot of people still say "jechać na saksy" when they talk about economic migrations.
The following user(s) said Thank You: Steven Boryk
It's the same Częstochowa's St. Zygmunt's church that I looked up the other day (on metryki.genealodzy.pl). As I wrote, according to the 1911 birth index there are Jan & Stefan Janik twins baptised here and also Adolf Janik, but they are of different parents.
The following user(s) said Thank You: Steven Boryk