Short answer = no.
Long haired answer is that you want a light weight oil for the flathead to shed some parasitic drag on the rotating assembly. Also, the thinner oil allows the builder to keep clearances considerably tighter (cylinder, valve guide, etc.) Stock class flathead engines are typically built for thinner oils. If it's got some time on it though, Medium weight oil will not hurt it. Always check with your builder before making changes like this though.