PS4 it has no chance of catching, I think I should've framed the question more as does it have a chance to catch the XBox One ... even that might be very hard ... MS will have a 28-30 million unit head start or thereabouts, that's pretty hard to catch up to.
Maybe a good case scenario for Nintendo is
PS4 - 100+ million
XB1 - 40 million
NX (Console only) - 30 million (?)
This is assuming no gimmick, but even with a gimmick I have to think this time around Sony/MS are not dumb enough to let Nintendo had a 3-4 year window on any kind of controller gimmick, they will copy anything legitimately novel/market impacting type of controller very quickly.
NX itself would have to be so different of type of "console" that it's virtually impossible to copy, I don't even think a controller gimmick will make the difference this time around. Can they do that though? I dunno, that's a tall order.