Will a 60D do?
If there is sufficient of light then then 60D might do that, just as the 7D or the 70D could do it over there. there is however no guarantee that you can do it from Canon, as it is not build in in the design of the camera. I am not aware which firmware this even might block, but I think Canon could have done this. Did you look at the quality of your link to digital picture? even in the center the sharpness is gone when you compare the 560mm with the 400mm.
It may be interesting from a technical Point of view if it works or not. But:
(My expierience is based on a 50d, with 300 2.8 IS (original one) and Ext 2x iii)
with extender one needs 3 stops more light, 2 stops get lost by the extender and with 2x maginifcation one needs 2x faster shutter Speed.
in a situation where ISO 400 works ISO 3200 would be necessary. this ISO value is already quite bad for a crop camera. Next the quality reduction by the extender and poor AF performance comes to the equation.
With all of this, in my expierience, the lighting situation must be really great that the extender gives a really better result than cropping, but the risk to completely loose the shot (by to finding the subject in the viewfinder until ist gone, by motion blur, by trying to low ISO, by poor AF, by bad framing, etc) is much higher.
means, for my use, i would ot nmeed a long reach tele combination with F8 opening on a crop camera, F5.6 is bad enough. Maybe with lots of practise, there may be a benefit in a 840mm F8 combination, but this needs lots of skill, ond if one has These skills, one knows how to handle the difficulties, and taping the extender may be the smallest difficulty