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Maybe it will. But I'm not too sure.
Depends on a variety of factors.
1) When Final Fantasy XV comes out.
2) How big of an opening will it have and its legs. Because XIII had a very, very strong opening. Terrible legs.
3) How much of an install base the PS4 has at that time, which maybe around the same as the PS3.

XIII sold close to 1.9 million in Japan (PS3 and 360 versions), and this is just physical. and while the PS4 is doing tremendously well worldwide, its down in its 22nd month compared to the PS3 was in Japan.
PS3 in September 2008, its 22nd month in Japan, was at 2.36 million.
PS4 as of now,December 2015, is in its 22nd month in Japan, is at 2.08 million. What does this have to do with XV you may ask, because I think this serves as an indicator that XV will most likely finish around the same, better, or worse than XIII, depending on marketing and reception.
PS3 got Final Fantasy XIII in December 2009, it's 3rd year. The PS4 has a high chance of getting XV next year. In fact, I think its been all but guaranteed given Square Enix asking fans if they prefer XV or Persona 5, which launches in either Summer or Fall next year. So XV might be closer to releasing than we think.
So I'll predict that XV finishes with a little over 2 million in Japan. I'll say 2.15 million (Physical + Digital
While this is going on, Splatoon will keep selling.
It was confirmed to have reached 1 million copies sold in Japan not too long ago, that was for physical and digital. And it will reach 1 million copies sold, just physical before the year ends.
The question remains of how it will perform in Japan throughout 2016. For comparision's sake, lets look at how Mario Kart 8 has done this year in Japan.
As of December 13th, 2015, Mario Kart 8 has sold 312,160 copies in Japan in 2015. And this is just for physical.
The reason I bring this up is because, if you compare the launches of Splatoon and Mario Kart 8 in Japan, back to back, Splatoon is tracking well ahead of Mario Kart 8. At the end of last year, Mario Kart 8 was at 844,134 copies sold, physically. Splatoon is ending the year at 1 million. And I think that next year, Splatoon will sell considerably more than the 312,160 copies in Japan that Mario Kart 8 did this year. So I'm gonna say that in 2016, in Japan, Splatoon will sell around 500,000 copies. Bring it's lifetime total sales in Japan at around 1.5 million.
Final Fantasy XIII did that many copies in just one week. So I expect similar results from XV, an incredibly strong opening, but weak legs.

So in the end, it'll come down to how well the PS4 is doing in Japan compared to the PS3. When Final Fantasy XV launches, and the legs of Splatoon. But based off of these estimates...
I don't think Splatoon will do it. I think it's too much of an uphill battle, and with NX lurking around the corner as well, that could also effect Splatoon's legs. That combined, with the legacy and power of the Final Fantasy brand, will be too much to overcome. I think Final Fantasy XV will finish with more than Splatoon.