FME Licensing Details
FME requires a licensed ArcGIS installation to support Geodatabase formats:
Personal Geodatabase (File and MDB)
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Reading: ArcView or ArcEngine level or higher
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Writing: ArcView or ArcEngine level or higher
SDE Geodatabase
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Reading: ArcView or ArcEngine level or higher
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Writing: ArcEditor or ArcEngine with the Geodatabase Update Extension
From the Esri ArcEngine FAQ page comes the additional information that an ArcEngine license cannot be deployed on a Server machine.
http://www.esri.com/software/arcgis/arcgisengine/common-questions.html
Esri ArcGIS Licensing
In addition, in the ArcGIS 10 help
here, can be found what geodatabase functionality is available at the various Esri ArcGIS license levels.