I do not have a direct connection between Charles Drott and Johann Adam Drott. However, I did see references to your Catherine Drott and did not find any other information on her until your query. The Ohio and Wisconsin Drott's as well as my great grandfather Johann came from Hesse.
The one clue that I have that Johann may be related to Charles is that in his New Orleans obituary there was a request to also print it in the St. Louis paper. ( 1885 )