You may want to take a look at this.
http://sourcegaming.info/2015/12/13/sakurai-fe25/
Specifically the section labeled
Playable fighters in Smash are influenced by the “trends of the time”
It really isn't just a matter of "oh, this game's out, so it's protagonist is going to make it in".
Had Awakening not release when it
did, for example, we would likely not have had Robin or Lucina.
And that applies to being released
earlier as well as later.
I actually agree with this and have practically believed it since the early days of Smash 4 speculation. A YouTuber by the name of ECCWii basically mentioned that each Smash kind of based new roster additions off of the past system. Based it off of characters, games, and franchises that made an impact leading up to the announcement and development of each Smash game. In the case of his video, Brawl. I went and looked at the roster again and pretty much went "Holy crap, he's right". Besides ROB, a retro character, all of the other newcomers had a big moment or made their debut during the days of the Gamecube, GBA, and DS (maybe some Wii as well).
Characters that stood out leading up to the announcement of Brawl or characters that stood out during its development. This doesn't confirm every character during that timeframe to be in Smash Bros but it gives you the chance to see who actually is possible.
When that happened I kind of took that mindset when speculating on Smash 4. I looked at characters like Chrom, Lucina, Robin, Palutena, Isa Jo, Matthew, Isaac, Andy, Shulk, Rosalina, Bowser Jr, Ghirahim, Villager, Mega-Man, etc because of games like Fire Emblem Awakening, Sin & Punishment Star Successor, Golden Sun Dark Dawn, Kid Icarus Uprising, Mega Man 9&10, anything Mario, Zelda Skyward Sword, Xenoblade, etc. And low and behold quite a few of them made it in. These characters that made their debut or had a big impact during the likes of the DS, Wii, and 3DS stood out because their releases times well up on Smash 4, its development and before.
I am not saying Fire Emblem 16 is almost guaranteed a character just because it is a new entree or just because it is the next game. I say that because, like you said, this game might be the only that fits in with the timing of Smash 5. It will be in the timeframe that Sakurai or Nintendo would try to look at. If Smash 5 comes out approximately the year difference between Melee and Brawl or the timespan between Brawl and Sm4sh a good guess is it will be 2020-2021.
FE16 is either going to be 2018 or in 2019, practically leading up to that putting it into a timeframe that makes sense as possible. The only thing that could really hurt it is if FE17 and/or FE18 (or beyond) come out because those then might fit the timing better during this likely Wii U/3DS/Switch approach to Smash 5. But that could all depend on when Smash 5 actually comes out and if those years are it or not, meaning more games being developed to look at.