A long time ago I did some successful moon shots with my 300 F4L + 1.4X TC + 2X II TC, although they required a fair bit of post processing and the resolution on my D30 wasn't great...
The other day I had a go, and it was only when putting my lens and TCs together on my partner's 1000D (since it's got higher pixel density and live view, which my 5D does not) that I realised I'd lent my 2X to my father, so didn't get the shots I wanted.
Generally, stacking TCs doesn't work brilliantly. Sharpness is dependant on the lens you start with of course, but the main problem I find is chromatic aberration. Since this is relatively easy to correct for in DPP now it could be less of an issue, but DPP will not recognise stacked TCs. Since the 2X II is the only one that natively stacks (ie you can add another TC to the back as it has a recessed element like TC-compatible lenses do) it's the 2X II that connects to the lens and is the TC identified by DPP - any further TCs closer to the body are not recognised. I suspect that playing with the CA slider in DPP will probably cover the bases however.
So yes, it can be done. It isn't, however, a great solution and will never be a patch on an 800 F5.6, or an astronomical telescope.