If you wire your winch to the starting battery on a stock setup 6.0 PSD, you are eventually going to a have a bad a day... It may not be a problem the first time you winch, but every time you winch, your chance of a problem goes up.
As you suspect, dropping supply voltage to the FICM is bad news. Most other vehicles are pretty much fail-safe from low starter battery voltage, because if the battery voltage is too low, the PCM will just turn itself off. The FICM will just cook itself instead.
That said.... there's more than one way to avoid this....
1) Install an aftermarket alternator that provides more power at idle.
2) Install a high-idle switch, and only winch using fast idle.
3) Install more or better batteries. Using house batteries is fine. But using the start batteries are fine too if you have a good separator and wiring that will keep it all in parallel while winching.
4) Do what you propose, and connect to house batteries with a cut-out... Downside is the length of wiring needed to reach most house batts. But the 6.0 starting batteries are remote as well. Either way make sure the wire gauge is sized for the extra distance.
5) Deep cycle batteries are good for starting too, provided they also output the CCA needed for your motor. When you winch, you may be deep cycling the battery, depending on the situation. With a regular starting battery, eventually it won't hold a charge anymore. Bad starting batteries are really the root cause FICM failures on rigs with high electric demands.
6) Install a more robust FICM
7) Test wet cell batteries periodically, using a carbon-pile tester (then recharge them with a charger!), and clean the terminals when you do that.
Any of the above will provide good insurance against FICM damage. Doing more than one is even better!
Also, winching methods will greatly change power demands from the winch. This higher the winch-line load, the higher the power demand. This is a good guide for winch-line forces:
The one thing not mentioned in that guide, is drum load forces. The more wraps around the drum, the harder it was to work. The manual that came with your winch describes that well.
Lastly, if you're only winch yourself, and you still have drive power, chances of exceeding the abilities of your charging system is low. But if you get stuck without drive power, or have to recover somebody else, or have to winch while pulling a trailer, or have to do multiple pulls... Your stock system probably won't keep up.