I'm not aware of any studies relating sfc low depth to severe weather, but I've had two "tornado days" with a sub-990mb surface low: 04/06/06 and 09/21/06. Both events had a surface low of 986mb.
As for yesterday, the sfc dewpoints rapidly mixed out into the 30s from the southwest.. IMO this left a very narrow juxtoposition of sufficiently low LCL heights and marginal 3km CAPE in the vicinity of the occluded front. The behavior of the storms seemed to support this theory. Not to mention, 1km SRH wasn't impressive due to the highly occluded nature of the low (though this naturally isn't a requirement in environments with high ambient vorticity), and instability was way overforecast due to the moisture mixing out. My 2 cents.
I agree with Chris that moisture can make or break the very intense systems/deep surface lows that are more common in the cool season. For instance, I can only assume the super outbreak (which had a sfc low in the low 980s I believe) was preceded by many days of return flow to get widespread rich BL moisture in place... possibly induced by a lead shortwave or two ejecting out of the mean trough position. This is an extreme example, of course.
Maybe it would be better to look at the deep surface low cases where BL moisture is sufficient but tornadogenesis fails?