Hi Scotty,
It's a weird one?!
From the looks of things there are 3 Broad Gullies in Nillumbik. 
There is one to the north which actually does cross Broad Gully Road; and is named on Mapsharevic
and there is another up near St Andrews North.
I suspect that the watercourse in question wasn't important enough to warrant a name prior to urbanisation and was simply given the unimaginative name of the major road it crossed (Broad Gully Road near Amaroo Court) when it was undergrounded by MMBW. This naming practice can be seen in other drains in the area such as the Bible Street Drain, Zig Zag Road Drain and Allendale Road drain to name a few.
I'll look into it via the Diamond Creek Catchment Study and other resources the next time i'm at Diamond Valley Library in search of a different name - as this kind of thing interests me. However, I suspect that history never got around to recording a name for the drain until it was too late. :/
Keep up the excellent work! Diamond Creek's never looked so good ;)