That seems unlikely as Dak already knows the offense and they would not want to drastically weaken the team by starting an inferior player just to send a message (especially when he gets paid the same amount regardless of whether he starts or not).
Hypothetical scenario. Dalton participates with the team in virtual meetings. He runs the first team offense in training camp. He starts the preseason games. Dalton has done everything asked of him and has made connections with the team.
Prescott decides to sign the tag before the last preseason game. Prescott plays a couple of series.
Opening week arrives. Who starts at QB?
If you are a new coach you may lose the respect of the team by selecting Prescott to start. McCarthy would need to start Dalton to show the team if you put in the work, you can be rewarded. McCarthy needs to show that there is no favoritism. It's year one for him.
Even if you believe Prescott is the better player, you can't lose your locker room in year one, week one. If this was Garrett in year 10, it wouldn't matter.
In this situation Dalton must start for the good of the team and most of all McCarthy.