According to Greg Aiello who was in the draft room, we apparently did:
“
I’m wide-eyed and in the draft room,” Aiello told Clark Judge of The Talk of Fame Network, “and I was a graduate of Note Dame. So I had a particular interest as we got into the third round — and our pick was coming up — in the guy at the top of our board, Joe Montana. I was curious what we were going to do.
“. . . Nobody, of course, knew that Joe Montana was going to become one of the all-time greats and a Pro Football Hall of Famer or he would have been already taken before the third round. Nevertheless, here we are. Here’s our pick, and there’s Joe Montana’s name at the top. And I remember Tom Landry saying, ‘Well, we have three quarterbacks better than him right now.’ In other words, why would we want to take him? He was talking about Roger Staubach, who was about to go into his final season, but nobody knew that, and he was 37 at that point and was a young 37 because he spent four years in the Navy before he started the NFL. The backup quarterback was Danny White, and the third quarterback was Glenn Carano, who’s best known now for being the father of the great mixed martial arts champion Gina Carano, but at that time, he was a second-round pick of the Cowboys in 1977 out of UNLV, and the Cowboys didn’t know really what they had with him. He was a highly rated talented, a second-round pick, so in Tom Landry’s mind, we had three guys better than this guy ranked in the third round, Joe Montana. So [the Cowboys] took a pass and violated our own system and took the next guy on the board, who happened to be Doug Cosbie, who it would turn out was a very good pick.
https://profootballtalk.nbcsports.c...n-for-cowboys-to-pass-on-joe-montana-in-1979/
The great Tom Landry thought Glenn Carano > Joe Montana.