Actually we call it a "Space Generator", and yes its role is to make a major contribution to that second, reverberant stream of sound.
In particular I’m wondering whether it would work with other mains speakers?
As currently configured for use with my own main speakers, probably not. But at some point I expect to introduce a general-purpose Space Generator which should work well with a usefully wide range of speakers.
If so, how difficult would it be to calibrate the SG so that it would appropriately complement the mains?
Excellent question!
The future general-purpose Space Generator will need quite a bit more adjustability than what I'm currently employing, as thus far I have known in advance what the off-axis characteristics of the main speakers (my own) are. Providing sufficient adjustability to get a good blend with a fairly wide range of mains will probably be the biggest challenge.
I’m assuming here that the mains would not be dipoles.
Yes, in general I would expect dipoles to already have plenty of second-stream (reverberant) energy, and ime too much can degrade clarity.
If you don't mind, what main speakers are you thinking of?