No, the paper records start in 1656, but some records are missing (baptisms 1708-1710, marriages 1702-1717, deaths 1694-1716). Seems like not all of the records were digitized.
There is a local family book containing information on over 4000 families from Obergrombach, but it's only available in some libraries in Germany. Additionally, there are some other publications on the history and families of Obergrombach. None of them is digitized, unfortunately.?