Depends on how you count, really. By revenue passenger-distance a fully merged JANA would be about #5 -- behind DLNW, AA, AFKL and UA. They would have about 100m passenger enplanements per year, though, which might edge out WN as #1 in the world. (I think WN is #1, anyway.)

That said, I don't think this would ever happen. Both carriers have been consolidating their international and domestic operations for a while now, and I don't see why they would suddenly choose to reverse that process. I find it more likely that JAL (and/or ANA, as required) would simply downsize -- perhaps spin off business units, maybe farm out more stuff to lower-cost divisions.

The Japanese tabloids come up with business conspiracy theories all the time...