In terms of boosting your own AC, the two features (Draconic Resilience and Mage Armor) will not stack. Each is worded as setting AC to 13+DEX, rather than increasing your AC by 3. (Contrast this with the wording of the previously mentioned Shield spell.)
So really, the only point of a draconic sorcerer learning Mage Armor would be buffing other people. In that regard, a sorcerer might actually be better than most casters, as the "Twinned" metamagic allows you to use one spell slot and 1 sorcery point to buff two creatures. If the target creatures don't have an existing source of AC beyond DEX, the increase from 10+DEX to 13+DEX for 8 hours without concentration could be a pretty good deal.
In a typical normal adventuring party, everyone will probably have a decent AC without such assistance, so the spell will probably see little use (something you really don't want for a Sorcerer, with your limited spells known). However, if you have an unarmored NPC companion of some sort (perhaps a mount, a familiar, a ranger's animal companion [maybe], or some noncombatant that you're protecting), the spell might have enough consistent targets to be worth knowing.
Additionally, if you're playing in an intrigue style campaign, walking around in armor or with shields might attract unwanted attention. In such cases, the spell might be very useful for helping out characters who would otherwise be relying on armor.