The thing even a hero requires actions on our part, which we both know we ain't gonna take unless we are forced, which we aren't due to the overflow
So the way I see it we take him, then don't take any culture actions because between dealing with factions, the nomads, the hamurri& freehills and whatever other fires might occur, people won't be willing to waste their precious few actions that they have left and then he dies and all we will have archieved is that we have wasted culture
If you really want to advance our culture then you would either go for a genius, who require much less action input from us to advance us if any at all with our innovation rolls or you go for the safe and sound cultural advancement in form of trait evolution