Regarding her assist: It has either no or very little invinisibility, it’s just very high priority, like psylocke’s AA.
I did some testing counter-calling Morrigan’s assist against various AAAs a few months ago. As I remember, it’s got slightly better priority than psylocke AA. It loses to cyclops, the shotos, cammy, jin, loses or trades with capcom (usually… capcom’s pretty random. Sometimes they just go through each other…), but it beats psylocke, doom, tron, charlie, guile, IM, WM, cable… Also beats most supers if called point blank before the flash.
Those teams look like fun (rushing like crazy!), though the Mag team may not be as effective as the one with Storm. I think the Mag team would be better played as Mag/Morrigan/Psy, so at least one of them will have a good frame-kill DHC to work with (tempest–>soul eraser). The Storm team should probably be played with Morrigan starting, for the silhouette blade–>hailstorm DHC.
Morrigan does pretty well with Storm’s projectile assist-- it helps keep them in blockstun so she can rush, and it can allow her to combo into darkness illusion or soul eraser pretty easily. You can also throw them onto storm’s assist with Morrigan’s HP throw, then launch or whatever.
All in all I don’t see Morrigan working as well with Mag/psy though-- his assists don’t help her as much as Sent’s, Storm’s, Tron’s, or most popular AAA’s and psy assist doesn’t benefit Morrigan nearly as much as it does Magneto (she needs something to keep them grounded, or to keep AA’s out of her hair, neither of which psy is very good at), and Morrigan’s assist definitely doesn’t help Mag’s as much as Psylocke’s, since Morrigan’s AA doesn’t really set up anything besides an iffy ROM opportunity. She can’t really take advantage of her frame kill abilities with Mag as a DHC, and while he can frame kill into her soul eraser pretty effectively, it’s not as usefull as, say, a hailstorm or proton cannon would be.
If you’re dead set on using Morrigan and Mag together, though, you might want to try using Sent-ground or Tron-projectile instead of psy as your main assist. This way both Morrigan and Mag will have an assist they work very well with, and if you use Sent the team will be effective no matter who’s on point. And while silhouette blade–>HSF may not be the best frame-kill DHC in the world, it’s at least decent at getting Morrigan out of a jam (better than psy would be IMO).