In my opinion the addition of additional brine will not do any harm as it's much more important to ensure the fermenting cabbage remains in contact with either brine or a CO2 saturated headspace. The partial freezing pre fermentation shouldn't hurt.
My original post, as quoted by @FauxPas, was concerned with frozen hot peppers destined for hot sauce, where after a post fermentation puree and straining out the solids, texture did not matter.
I'm also curious to how this will turn out.