Odds are (and please, somebody correct me if I'm wrong here) that the 10-14% Ni in the 316 is going to retard significantly (if not stop entirely) any carbon diffusion across the weld boundaries. What you'd end up with would be definite hard/soft zones.
There may also be issues of it wanting to destroy itself in quenching, but you'd have to experiment to see about that. I know that certain combinations of stainless and high carbon in a Foster-Style san-mai have caused the high carbon core to literally split down it's length.
-d