Shot the Moon with the Canon EF 600/4L IS and 1Ds camera at ISO 200. Added the 1.4xII, 2xII and then the two of them stacked together to yield a 1680mm f11. All photos taken using autofocus (central spot only), Aperture Priority (wide open) autoexposure (central spotmetering) with an extra 2/3 stop overexposure compensation, wobbly photo tripod (as lenses go, the 1Ds+600mm is quite heavy!), mirror pre-release. Deep Sky photos taken on other nights are also given as examples. The Moon shots should be enough to convince daytime shooters. For the much more demanding astro-imagers I'd say that basically, the Canon 600mm/4L IS can be used for DSO imaging without any qualms, with or without Canon tele-extenders, aperture wide open, on full 35mm format. Unfortunately when stacked extenders are used, 1680mm focal length, the focal ratio wide open is at f11, too slow for convenient DSO imaging. So I threw in an example of the Venus Transit. For successful astro-imaging of Deep Sky Objects, tens of long-exposure frames, typically 5-minutes each, have to be stacked to yield an integration time of hours, say, 3 to 15 hours exposure! The biggest challenge in such an undertaking is to have a mount that tracks the stars precisely, to the sub-pixel level. So showing 1:1 crops often demonstrates imprecise tracking, distributed over as many as 50 frames which very likely were aligned imperfectly, rather than lens deficiencies. Additionally, even showing a 1:1 corner crop of a short exposure on a star field cannot tell the whole story either. The corner stars will still look very good before contrast stretching, but when you use extremely severe contrast stretching, as is the case in all DSO imaging, the brighter stars in the corners will start showing gullwings and other optical aberrations, making straightforward comparisons to other lenses or telescopes of similarly high quality well nigh meaningless. Only way is to shoot the same starfield at the same location, same integration times and similar post processing. Nevertheless I believe that the examples I included here give a good appreciation of the fact that this lens+teleconverter(s) combo is unlikely to be the limiter in image quality for all but those rare, very accomplished astro-imagers, perhaps. There are only a handful of amateur-affordable astronomical telescopes that cover the full 35mm format as satisfactorily.

I have added a similar test using the Canon 200mm/2.8L II on a modified Canon 20D. This camera has no antialiaising filter but of course a 1.6x crop factor compared to a 1Ds. Surprisingly, the lens seems to be weakest off-axis at 200mm/2.8. The edges behave better relative to the center when extenders are used.

Finally, it is very important to realize that pixel size does matter when talking about extenders. If an excellent lens is capable of giving a star FWHM of between 10 and 15microns and you are sampling it with a 9-micron pixel pitch, it would be reasonable to expect some extra detail when we add a 1.4x extender (effective pixel pitch of 6.4 microns) but if we are already sampling the 10 micron FWHM stars with a 4 micron pixel pitch (2010 and later vintage Canon DSLRs) then, frankly, we are chasing the improbable. We should expect a stretched-balloon result when we use a tele-extender. Far better to simply crop.