As has been pointed out, Elway was never the coach. But he was the GM in charge of building and maintaining a winning roster.
In his first draft (2011), he drafted no quarterbacks.
In 2012, he drafted QB Brock Osweiler in the second round. Osweiler played four seasons with the Broncos, starting 7 games. But Elway also signed Peyton Manning in 2012, who led them to two Super Bowls, winning one. Osweiler played behind Manning for 3 seasons, and finally started half of their games in 2015. That was his last season in Denver; he was in the league for four more seasons.
In 2013 and 2014, Elway drafted no quarterbacks. In 2015, he drafted Trevor Siemien in the 7th round. Siemien was their starting quarterback for most of the 2016 and 2017 seasons, compiling a record of 19-14. Siemien is still in the league; last year he was with the Jets.
In 2016, Elway drafted Paxton Lynch in the first round. Lynch was the backup to Siemien for two seasons, with a starting qb record of 5-4. Those were his only two seasons in the NFL.
In 2017, Elway drafted Chad Kelly in the 7th round. His NFL career consists of one incompletion for the Broncos in 2018.
In 2018, Elway drafted no quarterbacks.
In 2019, Elway picked Drew Lock in the second round. He played for the Broncos for 3 seasons, compiling a record of 9-14. He went to Seattle in the Russell Wilson trade.
In 2020, Denver drafted no quarterbacks.
So while Elway was never the quarterback coach, it’s painfully obvious that he also had no eye for talent, as all of his draft choices were failures of varying degrees. HIs one bright spot was signing Manning, so he does get major kudos for that move. But the draft? Not so much.