Absolutely not.
The winch needs to cool down between short burst pulls. The stock alternator can easily keep up during the cooling periods.
I hooked up a regular hand held volt meter to the winch battery and mounted it in the cab so I could see the exact voltage during winching and resting. When the batt voltage dropped to a certain level I would stop winching and let the batt recharge & winch cool down.
In my experience its winch heat that's the limiting factor, not alternator size. You've got to wait quite a while for things to cool down between short pulls or you might pay the ultimate price.
I also mounted a small 12v fan next to the winch to help cool it faster.
I had 2 batteries hooked up in parallel.