Do you have a minimum TOC value below which generation just cannot happen

There is no fixed lower limit to the TOC in order for generation to occur. But if both the TOC and HI values are very low, there is a chance  that all of the generated HC will be retained without any expulsion out of the source rock.  You can also adjust the threshold for expulsion by setting the Oil.retain and Gas.retain parameters (thus making the source rock more effective).