Do ArcGIS Online basemaps support the Tile Resampling capability?

Yes. As of February 21, 2014, after a basemap system upgrade to ArcGIS for Server 10.2, ArcGIS Online supports the Tile Resampling capability for the following basemaps:

• Topographic
• Street
• Imagery
• Imagery with Labels 

With the Tile Resampling capability, most Map data not yet available tiles no longer display when the maximum resolution of data is exceeded in isolated locations.

The Tile Resampling capability is automatically enabled with the system upgrade. Therefore, no action is required by the user.