Can I use my alternator to recharge a discharged battery?

Answer:

Possibly; but at a cost you may not want to pay...

When installing an alternator, the battery should be fully recharged before starting or driving the vehicle.
In many cases, depending upon how thoroughly discharged the battery is, it can take 4-8 hours.
Most technicians and DIYers don’t want to wait that long so they just get the vehicle running, and figure that by driving the car around the alternator will charge the battery.
In some cases with weather extremes the battery never gets fully charged, and in all cases the alternator is being overly stressed demanding it do a job it was not designed to do.
This leads to premature failure...

Ask me how I learned this.....