As it turns out you can create a contour of a focal statistic without persisting to disc, consider this example:
This creates a Focal Mean of a 3 x 3 cell neighborhood on the fly and contours that to a 50cm interval.
You must do this in a script or in the python window of ArcCatalog/ArcMap, the objects don't exist in modelbuilder or the toolbox unless they're persisted (written permanently) to disc.
As I said in my comment, this will (may) not speed up the process but will reduce the disc footprint of the unwanted focal statistic rasters. The temporary rasters are stored in your arcpy.env.scratchWorkspace in GRID format, which may be quicker than compressed file GDB raster at processing but because the raster is removed as soon as the process completes you could set the scratch workspace to a local, small, fast drive like a RAM Drive if your rasters/tiles are generally small enough to fit into memory; in some cases the data drives of workstations are RAIDed and might be faster (and larger) than C:\users\your_name\AppData\Local\Temp which is the default Windows %Temp% drive setting your scratch workspace to a folder on the array will (could) result in a performance increase.