Technically speaking, with a remote login app and a desktop you could, but not on the device alone. To the best of my knowledge, there is not a single app in the android playstore that allows you to make footnotes, and in iOS I think there is only one: Pages. This is one of the reasons I have an iPad and not a Nexus 10.
As for writing your dissertation on the iPad, you certainly can, and I have (the vast majority of it anyhow). With a bluetooth keyboard, it's easy, and quite a bit more powerful than the computers I started out with just a few years ago!
But if my memory is correct, you were using the iPad to write your thesis even before Pages had footnote function, right? So Android tablrts may be a step behind, but I'm not sure why you are ruling them out so completely.
Reading these older threads make me appreciate how far the iPad and iOS have come since they were first introduced. Like Pages gaining footnote function, for instance, but so many features have been added, that a lot of things that couldn't be done back then can't be done now. People not realizing they are responding to old threads would often be like, "Well, of course you can do X!" but it couldn't be done back then. Yes, the iPad is definitely more powerful than my first computers, lol.
That said, I know I've said this before, but i don't think I'd like to work on a dissertation on an iPad. I don't write anything long right now, but to me, editing a long document on a small screen is a pain. I don't like doing that even on my 13 inch Air. I can see myself hammering out a first draft on my iPad, and I think the iPad would be invaluable as a note-taking and record-keeping device -- I realy wish I had had an iPad when I was doing library research! But once the research and the first rough ideas have been written out, I think the iMac would be my device of choice for editing and fine tuning my paper. I love how I can actually see and read a whole page of text on the 27-inch screen. It's so much easier to keep my place in the flow of ideas that way.
Overall, the iPad is a very welcome addition to my electronic tools, and is easily my most frequently used device, but the desktop computer and laptop haven't lost their importance in my life, either, because I'll always need a larger screen device in order to work efficiently.