No, the Spider at Melb Luna Park was installed after the demolition of the Rotor, in the 1970's.
I never knew about LPM Spider being ex-Witts, but this doesn't surprise me.
Yes during the 1980's, Wittingslow had a 49% stake in Luna Park Melbourne, but sold out by about 1993. For many years they regularly alternated their travelling rides, providing regular variety. The current Galaxy Coaster and Enterprise were once owned by Wittingslow, and sold onto the park.
Likewise, with the 1995 refurbishment of LPS, Wittingslow owned a stake in it, in fact, Ranger, UFO, Breakdance and a number of kiddy rides that are there today, were ex-Wittingslow.
I have a feeling the Wonderland Funnel Web become a travelling unit. I remember one that was at the Melbourne Zoo in the early 1990's that could well have been it.