Thank you for the information.
I was able to solve my issue. I found that the problem was due to the extent I was supplying to the GeodatabaseSyncTask. I was capturing the extent of the map when online and supplying that. The base map was causing that extent to be in a different spatial reference than the feature data so the GeodatabaseSyncTask wasn't downloading anything.
To solve the issue I used GeometryEngine to project the envelope from the original map extent to the feature extent. I then supplied GeodatabaseSyncTask with the new projected extent and output to the original map extent. The data displayed correctly then.
Thanks for your help,
Brian