Not really. It began as post-launch content for Titanfall 2. They didn't change the genre to battle royale, they were making a BR as an additionnal game mode for Titanfall 2.
Perhaps this game mode would have only been released later in a potential Titanfall 3 if they didn't focus so much on it, but it was never meant to be TF3 all by itself.
https://www.ea.com/games/apex-legends/news/two-years-of-apex-legends
Just to clarify it was never post-launch content for TF2; it was part of the new idea exploration that took place while TF2 post launch content was wrapping up. There were numerous small groups of devs working on many such experiments simultaneously, but all were in the context of possible content for TF3.
Regarding TF3; I think what people don't realize is that the team that made TF/TF2 (and COD through MW2) is all but gone from Respawn at this point. (it would be interesting to see a comparison of credits vs. "where are they now?") If Respawn were (or are) making it, it would almost certainly be a new take by a new group of developers. That doesn't mean it wouldn't be good, but it definitely wouldn't be the same.
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