A pretty unlikely scenario.
I don't know if he was completely healthy since the 2010 season. Many times after that, he was hailed for his grit and ability to play with pain. Then he got hurt again in 2015 and things got a lot worse. So, in the context of "healthy", those injuries effected him permanently, especially the most recent in 2015.
Therefore, the most realistic possibility would have been that Romo was healthy.....according to Jerry Jones.
So lets assume that he doesn't go down the first time he is hit. Here goes:
His mobility was gone by 2016. There were several occasions where Dak made a great play that involved a lot of running, plays that determined the outcome of the game, plays Romo couldn't make and shouldn't even try.
In addition, the offense would not have been as physical in the running game. This isn't really Romoi's fault, it's just a by-product of him being the starter instead of Dak.
You see, because Dak was an inexperienced rookie, the Cowboys had no choice but to place a heavy emphasis on the running game, which they should have, considering the RB and the O-line. Also, they placed an emphasis on ball security by instructing Dak to avoid risky throws. They limited their number of pass attempts, speeding up the clock and providing less time for opponent offenses. This turned out to be the perfect recipe for that 11 game winning streak.
Here is the big question:
Would the Cowboys young OC, Kellen Moore, be satisfied with a run heavy offense if he had Romo for each game? I think not. Moore is a disciple of Jason Garrett who would kill a running attack after the first 1 yard loss..
This would have halted the O-line's attack mentality that dominated defensive lines in 2016. Remember that was the year all three of those guys made 1st team All Pro. They were also excellent pass blockers but that wasn't the reason they were all recognized.as the best at each of their individual positions in the NFL
So the offense would have passed more. Romo would have had more freedom to make certain throws. He wouldn't always make them. There would be more turnovers which was Romo's trend during those times he did play in 2015.....4 starts.....7 INT's.
There would have been shorter, less time consuming drives which meant the opponent offense would have more time to bully a rather hapless defense at the time.
I don't think Romo could have inspired the team as much as the rookie duo of Zeke and Dak. It was a pretty special story.
They may have had a winning season, maybe. I don't think Romo would have matched or surpassed what the Cowboys did that season with their unlikely starter at QB, a rookie 4th round pick.