A 12 volt alternator cannot charge both batteries in a 24 volt system at the same time. It would have to charge one, then the other.
When winching with a standard 12 volt or 24 volt system, a significant portion of the winch power is directly provided by the alternator. Without the alternator simultaneously charging both batteries, one will be required to supply the ENTIRE current required by the winch. Thus it will discharge rapidly. If the one battery gets depleted, the remaining battery and the alternator will reverse charge it and destroy it, which could cause a fire or explosion.
It can be done, but it is extremely difficult to do safely.