Is is possible to have a battery powered alternator to power the electrics of the car as well as recharge the batteries that power it?

 

No.

Why?

You hook up an inverter to your batteries and then plug a battery charger into it to recharge the batteries that are running the inverter. LOL With actual efficiency at 75% you get dead batteries!!!! There is no free lunch if thats what your asking.

 

You would still need an additional electric motor to spin your alternator, and this would take a huge draw from the batteries, moreso than you could recharge through the alternator. Now if you could run it off some kind of fuel cell...

 

What you are suggesting falls under the general classification of "perpetual motion machines", and violates some of the laws of nature our universe is subject to. Maybe somewhere in a parallel universe... (why is it you never hear of a perpendicular universe?)