I think not only should you not see the DC, you should not even be aware that you rolled. Out of dialogue rolls should be fully invisible, in dialogue rolls should not be marked with persuasion or race or class tags. It should all simply be natural and flowing and whether you got a good or bad outcome or whether you picked an option with only one outcome, it should all be hidden. This would add to the mystery and immersion of the experience, as those bits of information - whether its a roll, what skill or tag its using - they modify your likeliness take an option. How could one see a rare multi-tag combo option and not feel compelled to take it?
This complete roll blindness should be an option you can turn on at the start of the game.
