This is looking increasingly likely - here's a recent nature paper showing these organoids are electrically active, recording spikes from a dense 256ch electrode. That team also was able stimulate optogenetically yielding bidirectional communication with an organoid - http://www.nature.com/nature/journal/vaop/ncurrent/full/natu...
Another interesting paper demonstrating that neural tissues can be effectively grown around mesh electrodes, providing both a scaffolding function as well a recording and stimulation functions. http://faculty.engr.utexas.edu/xie/xie/publications/ultrafle...
Neuroscience has been rapidly leveling up recently, its increasingly believable that high bandwidth bidirectional neural interfaces (at the cellular level) are on the horizon. DARPA was pitching this a few years ago (NESD) and it was pretty far out, but now see Kernel and Neuralink and the 10 or so companies partnered in to those efforts mostly-successfully developing all kinds of technologies required by this roadmap (disclosure: including my own).
After Elon Musk's Neuralink figures out a scalable way to interface with neurons. Need probably millions of electrodes, not just a few hundred like we use today.
It would be kind of crazy if we develop full AI by literally using brains in vats. But it makes sense (even if it is horrifying). Meat is cheap, and the brain is like an exa-OPS computer running on 20 Watts of power. If you could solve the interface problem and figure out how to actually use it practically, brain is like 6 or 7 orders of magnitude cheaper than the next-cheapest computing substrate. That's like half a century of Moore's Law (and Moore's Law is basically over now... much slower pace, at least).
While dead brains might be cheaper than electronic, I doubt that growing neurons in a lattice and doing what you want will ever be.
There is some research going on in using spintronics for neural network, and I think that both density and power usage would be a fraction of a biological system.
There is probably a long way until we can emulate human brains, but for generic neutral networks, I think electronics or spintronics is the probable route.
Brains are not general purpose computers though. You could probably train lumps of brain tissue do to certain tasks, but putting any kinds of FLOP/s numbers on the label is like stating horse power for levers.
That's why I said "OPS" instead of FLOPS. The kind of operations that brains are good at are orthogonal to the kinds that computers are good at, so a hybrid approach is probably a good idea. Again, I'm primarily thinking about this for AI type applications, not like fluid dynamics or other applications requiring high precision.
EDIT:And technically brains are general computing devices. Just really inefficient ones. Emulating logic in wetware is highly inefficient (and usually requires an external memory device, like pen and paper, though pure wetware memory also works in some especially skilled individuals, although still with severe capacity limitations). Of course, emulating wetware in logic isn't terribly efficient, either.
Some years ago (9+) Professor DeMarse published some papers on training petri dish brains cells how to "fly a plane" (or more appropriately "keep a simulated plane from crashing"). I have a copy of the paper at home, but can't think of the title, (it was kind of hard to find a copy since it wasn't publicly available online). You might look at what his lab is currently working on though.
Another interesting paper demonstrating that neural tissues can be effectively grown around mesh electrodes, providing both a scaffolding function as well a recording and stimulation functions. http://faculty.engr.utexas.edu/xie/xie/publications/ultrafle...
Neuroscience has been rapidly leveling up recently, its increasingly believable that high bandwidth bidirectional neural interfaces (at the cellular level) are on the horizon. DARPA was pitching this a few years ago (NESD) and it was pretty far out, but now see Kernel and Neuralink and the 10 or so companies partnered in to those efforts mostly-successfully developing all kinds of technologies required by this roadmap (disclosure: including my own).