Resting potential of an average neuron is about -70 mV. The peak of the action potential is at about 50 mV–a total swing of around 0.12 V.
My guess would be, simply: no. The chip would be highly unlikely to respond to potential changes in neurons, and as the chip you’re postulating has no power source, there’s no way for the chip to transmit a signal to the neurons.
(Aside: at least, not a signal that makes any sense. I have a small bit of surgical steel in the midst of my brain, and it’s credited with causing the seizures I had several years ago. Eddy currents and minor currents can appear in the metal of a chip due to fluctuations in the local electric fields, but they wouldn’t be useful in an information capacity.)
To call this an oversimplification would be a major understatement. Your average cortical neuron has input from around 10000 other neurons, both near it and from far away. Some of these inputs are excitatory; some are inhibitory (that is, some of the inputs decrease the cell potential.) In the simplest system, several excitatory inputs will cause an action potential, but it should be noted that the AP is only a rapid change in the local potential.
I tend to think of an average neuron as equivalent to something around ten thousand very slow transistors, because each ion channel and cascading signalling pathway is a single switch–a single chemical transistor, if you will. There is also the added bit of long-term potentiation or long-term depression (the cellular memory that Arjuna mentioned), which depends on certain patterns of firing (and could be vaguely compared to computer RAM).
We’re at least decades away from merging silicon chips with neurons for anything but limited functions. It would be easier, IMO, to build an entire brain from silicon chips, though it would, as Arjuna noted, be significantly larger than your brain.
LL <-- SDMB resident neuroscientist