I'm guessing a complete nightmare (note i speak from a position of complete ignorance on this).
But well done for raising this as I bet all the early music/baroque folks are now racing to their luthiers to get their instruments just that bit more authentic
I'd imagine you'd suffer all the instability of a gut string, but across the whole 4. Although presumably they would all detune by the same amount?
Back to your question. I'd love to believe it would impact on tone in a good way.