Hypothetically speaking, if we develop a sufficient understanding of analogue information processing, couldn't we build either (a) some kind of analog co-processor that operates in this manner and interfaces with the computer, or even (b) a sufficiently precise digital simulation of a system that can use analogue processes?
Maybe we can. I hope we'll invest in finding out, and soon. Then again, John McCarthy doesn't seem to agree, as this answer suggests:
Q. Is there anything in principle that would prevent a computer from thinking as a human would?
A. No
IOW, there's still no recognition today, on the side of the purveyors of "classical" AI, that anything except digital processing might be needed for a computer to think "as a human would". So the big money is likely to continue being thrown at attempts to emulate animal brains using purely digital means. And I suspect that these funds might largely be better spent elsewhere.
I tried to find a free PDF version of that paper, but no such luck. However, I found an earlier one by Michael Spivey and Rick Dale, ON THE CONTINUITY OF MIND: TOWARD A
DYNAMICAL ACCOUNT OF COGNITION (59 pages, <http://www.cogstud.cornell.edu/spiveylab/PLM.pdf>;).
[1] Spivey, M., Grosjean, M. & Knoblich, G. (2005). Continuous attraction toward phonological competitors. Proceedings of the National Academy of Sciences, 102(29), 10393-10398.