It's not easy just to switch to QGIS if you've decided to stay invested in the Arc-Geodatabase. I would say don't switch. You'll have more trouble mixing the technologies than it would be worth.
The ESRI Geodatabase is a database meant to work with the ESRI platform. Although there is a 'plugin' for QGIS to use a file geodatabase, there is (as suggested above) no editing capabilities within QGIS, and I see many bugs reported on this forum relating to QGIS and the File Geodatabase. (Additionally, see the note at the bottom of this reply on simply moving workflows to open source...)
For us, we're switching to a spatial database workflow, rather than a geodatabase workflow. This means moving data into Microsoft SQL Spatial so we can use the SQL spatial capabilities of a spatial database. This workflow is based on PostGIS and an enterprise system where spatial data is treated like any other kind of data (versus a model where spatial data is the main data type, and anything else is just an 'attribute').
However, although we're still able to utilize the power of the spatial database, we can still bring the results of queries, custom spatial tables built on SQL views containing spatial data, etc., into ArcMap for visualization and other geoprocessing analysis, as well as publishing these tables to ArcGIS Server.
Why can't we move to open source? Our student information system is based on Microsoft SQL Server. Switching to a full open source stack would cut the ties to this system (for example: PostgreSQL doesn't have a MSSQL wrapper, and I don't want to pull millions of records into Postgresql on a regular basis when the proprietary stack we have works just fine for what we have). If I had my way, the entire system would reside in open source, from the database to the desktop 'GIS' client, to the map server, to the front end. I don't even want to use the Leaflet API for ArcGIS server because it doesn't have query tasks!
There's lots of talk of blending the open source and proprietary models, but I'm not for it. As I've said on this forum before, simply switching the workflows of ArcGIS to open source software doesn't give the full power of the open source geospatial workflow a system like PostGIS offers...