A static copy couldn't learn, think, or experience time. A static copy is inert. I could imagine horcrux-magic automatically overwriting the brains of people who come into contact with them, so that Quirrell would become Voldemort, but the horcrux can't be static if Quirrell is still present in lobotomized form. In that scenario, neither one is a running copy of Voldemort.

But the idea of horcruxes as copies may be correct.

"Harry, how could Voldemort have survived the death of his body if he did not have a soul?" [...] "Good question," Harry said, after some internal debate about how to proceed. "Maybe he found some way of duplicating the power of the Resurrection Stone, only he loaded it in advance with a complete copy of his brain state. Or something like that."

If he didn't die at Godric's Hollow, perhaps he rescued Bellatrix to create a flesh and blood copy of himself from one of his horcruxes, and we really will be treated to the sight of two Voldemorts betraying each other. I'd like that.