We've been discussing this.
From a purely logical standpoint, they're bound to have an interest in this event. There is a question as to whether or not they will be aware that there is another dragonborn around, whether they will understand that it's the first dragonborn, and what they would do about it.
Since he's an ex - dragon priest who fought the dragons, they'll like him in that respect. What his plans are and how the Blades would feel about those plans is a very open question.