Most of the NZ Super Rugby sides are owned by their local Unions, like how the WAFC own the West Coast Eagles and Dockers. I think the Highlanders are the exception, or at least that the local Union are minority shareholders of them now, and I don't know about Moana Pasifika but who gives a f**k about them anyway.
Given that fact I think it's extremely unlikely that you'll ever see any of them look into starting an NRL side, and I highly doubt that most of them could afford it anyway. The NZRU would definitely try to stop them as well, whether or not they'd legally be able to do that in NZ IDK though.
If any of the NZ Super sides were truly interested in becoming multisport clubs, then they'd almost certainly look at options with lower start up costs like Basketball, Netball, etc, first before exploring the NRL as a opportunity as well.
So yeah, suggestions that it's likely that NZ Super Rugby sides would look into investing in NRL sides are fanciful at best.