That would be cool, BUT...
The first FNaF song actually fit the movie thematically.
(SPOILER WARNING IF YOU SOMEHOW HAVEN'T SEEN THE MOVIE YET)
"We're waiting every night to finally roam and invite newcomers to play with us, for many years we've been all alone" They've been trapped in the pizzeria and for the first time in years, they felt true happiness when Abby played with them, so they want her to join them.
"We're forced to be still and play the same songs..." The animatronics perform 2 different songs throughout the movie, "Talking in Your Sleep", by The Romantics and "Real Wild Child (Wild One)" by Iggy Pop.
"...since that day an impostor took our live away, now we're stuck here to decay." First one is pretty obvious if you know literally anything about FNaF. "Now we're stuck here to decay" is a reference to the end of the movie, as they decay and become the withered animatronics.
"We're poor little souls Who have lost all control And we're forced here to take that role We've been all alone Stuck in our little zone Since 1987." Everything here is self-explanatory except the 1987 part. Just wanted to inform you that the FNaF movie novelization confirms that the MCI happened in 1987 in the film universe.
All of this taken into consideration, I feel like there are better options than "It's Been So Long". It wouldn't be played off as brilliantly as the first movie because the song is about a mom losing her son. I'm still gonna cheer if it happens tho.