From what I can gather, yes. Access warehouses can be read and written with an FME Professional license, for SQL Server warehouses you'll need an FME ESRI edition to write, according to the formats matrix that is, the documentation states you'll need an FME Database edition, can you check this please @Mark2AtSafe
Thanks for the help. What I am really looking for is to use an FME connection in GeoMedia Professional to read an number of feature classes in ArcSDE on Oracle. Does anyone have any experience with that? Would that pose any compatibility problems?
From what I can gather, yes. Access warehouses can be read and written with an FME Professional license, for SQL Server warehouses you'll need an FME ESRI edition to write, according to the formats matrix that is, the documentation states you'll need an FME Database edition, can you check this please @Mark2AtSafe
Please see this article for up-to-date information:
https://knowledge.safe.com/articles/207/fme-and-intergraph-geomedia-compatibility.html
As of this writing, FME 2017 is listed as compatible with GeoMedia 2014.