Dead original iPad: should it work plugged in but with dead battery?

I worked on a dead iPad today. The owner thought the battery was dead and so brought a replacement obtained from eBay (in fact, a complete rear shell with battery still glued in place). The original battery indeed read 0V - evidently it'd gone into protective hibernation, but the replacement read 2.5V - probably on the verge of going into hibernation. (Probably not a lot of life left in it, but that's not my concern for the moment.)

We replaced the battery and put it all back together, but still no sign of life. We tried with it plugged into a 1A powebank but still the same. I suspect either a faulty logic board or faulty screen. I'll advise the owner to see if iTunes will recognise it.

But first, my question: should an original iPod boot up when plugged in even with a dead or fully discharged battery (as an iPhone 4 does but not an iPhone 5, to my recollection)?