My answer is, Hel yeah!

Here's an idea:

Though sorcerors have been welcomed, half-dragons are very rare, and none have come to the city in a century. The party's patron realizes that having one arrive at this point in time could de-stabilize the magocracy and give his nation breathing room.

The PCs are tasked with finding a HD rumored to live in the desolate mountains over yonder, groom him to become a pawn in their scheme, then present him to a house that was recently humiliated by the queen.

Beyond his breeding potential and his combat prowess, he could be a direct threat to the queen as a rival for her throne. He could also be an indirect threat as his children would likely displace hers in the next generation. The other clans would see opportunities to advance their own agendas.

The trick for the PCs would be to destabilize the nation without tipping it into a war from which one faction might emerge as the ruler of a unified kingdom.