Is there any kind of damage caused by aging which doesn't affect the brain?
Good question. Everything is so interconnected. It makes these analytic questions murky. I would guess there have got to be some organ-specific issues that don't apply. For example diabetes -- yes, I believe that your vat might be able to manage its fluid glucose levels fairly well. But immune senescence? How does your vat intend to provide immunity? If it does that in some way that approximates *all* the functions of a natural immune system, that's a nice goal to have, but I don't find it nearly as tractable a problem as glucose levels. *All* its functions of the immune system would be a lot of crazy interrelated functions you know... You'd have to build something that's somehow "good enough", but that's very, very hard, and the details aren't in any way clear to me today. Could it be easier than keeping the body alive indefinitely in its current form? Yeah sure. Could well be. It depends on the details. Those would need to be figured out as one goes along.
Or how about visceral fat -- the professors tell us that visceral fat exerts its detrimental effects by and large via messing with our cytokine signaling... So if that's the case, then presumably our vat would make sure that the brain sees a signaling environment that appears to it as coming from a young, lean body. That would be fabulous, but we don't know what cytokine profile would accomplish that, how responsive to various contexts it needs to be, and what it might take to build such a thing. How hard would it be to build a control system that we presently have no idea what it involves? Again, if we try to examine the details, we find ourselves in way over our heads very quickly.
Maybe a different way to think about it would be to look at it in terms of major causes of death today. First, we have heart disease -- does that seem to apply in the brain in the vat? Well, most heart disease is ischemic (vascular aging), and yes that happens in the brain in a very similar way, and gives us ischemic strokes. So if you keep your vascular system, that's a big one. Second is cancer. Cancer in the brain comes from stem cells, glia, and sometimes the vascular system. So again, if you intend to keep those things around, rather than replace them with yet-to-be-defined vat functions, those cells might presumably still be able to go rogue on you. Then there's neurodegeneration. We don't have much of a clue how that might be caused, other than the genetic association with ApoE. If it's caused by bloodborne factors (ApoE expressed by macrophage/microglia...?), then there might be more hope for replacing those than if it's neuronal factors (ApoE expressed by neurons...?). We just don't know... Accidents, homicide. We're all going to be sitting in steely super robot war machines, so let's not worry about those. Oh wait..!
It's a very important question. I can't begin to try to answer it. I think it's very helpful to view our activities against the backdrop of your all-encompassing question.