Formula One cars use a device called the MGU-H (uh... Google says Motor Generator Unit - Heat) to harvest energy from the turbo and to enable quicker spool up at transitional rpm. So yes, the possibility is there.
But these units are pretty high-tech stuff... there's a big electric motor splitting the intake and exhaust sides of the turbo, spinning at 100,000 rpm.
I doubt you'll be able to make enough electricity off a regular turbo to replace your alternator... unless you're driving at full boost, all the time.
Turbo boost is "free" power only in the sense that the boost the turbo provides counteracts the extra backpressure created by the turbo. If you disconnect the intake side, you're just making the engine work harder to spin those exhaust turbines. Probably won't be as efficient as an actual alternator.
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