In ANH Obi-Wan described Vader as having hunted down the Jedi, so your idea conflicts with that.
Also, so… Obi-Wan’s lying to Padmé to locate Anakin?
I can’t believe I’m engaging with Testing again but… plenty of Jedi survived Order 66. In both the old EU and the current canon, there are many comics and stories of Vader finding and killing these survivors. Vader killing most of them when they were all rounded up in a temple is barely “hunting down” to begin with!
Okay, but how would Obi-Wan know about that?
I consider this another bonus to the idea since it leads the audience to imagine events between films instead of connecting every dot like the audience is comprised entirely of infants.