sbaker62,
I will say this, Bore Butter is the most loved/hated muzzleloader product ever made. I used it back in the late 80's and early 90's on some blued guns but not stainless. I personally don't care for it at all and will never use it again. With that said, I know guys that swear by it and love the stuff.
I guess it will ultimately be your decision, but I really don't think it's needed. I have a SS Huntsman and clean the barrel with hot water and a few drops of Dawn dish soap. After cleaning, I rinse with HOT water. If your barrel is hot the water will mostly evaporate by the time you patch it dry. Then I run a patch coated with Break Free CLP (cleaner, lubricant, preservative) and lightly coat the outside of barrel/receiver with same for storage.
When I am ready to shoot, I run a couple dry patches to remove as much Break Free as possible. Then I run a alcohol patch to totally remove any oils. The alcohol will evaporate, then I pop off a couple caps to make sure everything is clear and dry. Load and shoot. :grin:
Never had a speck of rust using this method. Yes, stainless can rust too. :wink: