Nah, when you look at the team's record with and without him in that era it was night and day. He wasn't without flaws but he was a very good QB and we didn't put enough players around him as some of the old guard started to deteriorate.
You can include him as a major part of that old guard.
He was a fine QB, at times exceptional even, but the end of 1983 showed his will had cracked. We should have gotten him some counseling after he was crying on the sidelines after the 82-83 playoff loss to Washington, but we kept cooking.
Our half-assed way of challenging the position was to draft Gary Hogeboom, and he was average.
By the time White regained his confidence and won his job back, his arm was shot.
God gave us an easy button to fix it-- Boomer Esiason was there for the taking in 1984, and we ignored it and still started "Hogenbloom "/White with no real replacement in development beyond the abysmal Steve Pelleur.
In 1985, Landry at last recognized White's arm was toast and shortened the WR patterns across the offense. Our offensive stats shot to #1 overall for a time, until teams figured it out. By that time our defense was ancient too. The Bengals, Bears, and Rams ran all over us in 85.
Why for the love of God they kept White as a starter in both 86 and 87 is an unfathomable mystery. But it almost didn't matter because we stunk all over by this time, even after drafting Herschel Walker and Mike Sherrard. Aging Tony Hill. Ancient Randy White and Ed Jones. I can recall White absolutely heaving rainbows you could time with a calendar trying to throw deep to Sherrard. It was embarrassing.
When they finally made White a backup in 1988 it didn't matter. Pelluer was awful, and we went 3-13.