I don’t think he will unless it is on the old timer vote 30+ years from now. I don’t see him as an elite QB of his era (not over Brady, Manning, Brees, Favre…). Being a 2nd tier means he either needs a long career of great success (the Moon vote) which his wasn’t long enough or successful enough in my opinion, or the great playoff performances (the Aikman vote) which he doesn’t have either. Warner has the elite playoff vote in my opinion over him as well, so he falls down out of the top 5 during the majority of his career.
He did a lot without great WR’s for a lot of his career, but Andy has always seem to have gotten a lot out of his QB’s. And he did have some very good RB/TE weapons in the passing game as well as a well coached and somewhat talented line to work with.