Apparently there seems no such possiblity.
In the official apple profile manager help site you can have a look at the list of settings available to configure with Profile manager. They are listed under Configuration profile reference in various categories. As far as I can see, there is no such option available.
The full list can be seen here:
https://help.apple.com/profilemanager/mac/4.2/?lang=en
As for the "Trust this Computer" message, here is what Apple says: ‘Trust This Computer‘ alert on iPhone, iPad, or iPod touch
According to that article:
If you tap Trust, the computer will be trusted until you untrust all
computers or you erase the device. If you tap Don't Trust, you'll see
this alert each time you connect your device to that computer.