In a word yes.
It is the battery that will deliver the necesssary amps to drive the winch so this needs to be man enough. A 9500lb winch at full pull will use over 500 amps so a battery of 650cca minimum is recommended (by Warn). Obviously the winch will not need to work this hard often if at all so you are more likely to only use half of that (250amp).
The alternator will obviously need to replenish this when you are not winching. The bigger the alternator the faster the charge rate, so a small alternator will do, it will just take longer.
It is not recommended to run electric winches too long to allow for the heat generated to be dissapated and to allow for the battery to recover.


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