Mage armor is a magical force with no weight to it. It is not real armor. Unarmored Defense for a monk means being able to freely move, so mage armor does not interfere with Unarmored Defense.
So to agree with the previous post, yes you are changing base AC once to 13 and adding your dexterity modifier as normal for mage armor, then adding your wisdom modifier for Unarmed Defense. Furthermore, if you use the dual wielder trait and are fighting with two weapons, you can get another +1 to AC.
Now as a DM if my player does this and I let him, he is very happy.
Also it makes sense to us aesthetically. Now it is up to the DM to come up with ways to make encounters still fun and challenging. No need to be a rules lawyer; just have fun, especially with newer players.