It could if SDQ's fees are lower than Puerto Rico's.
There are no major Dominican airlines at the moment (Air Santo Domingo back away from NYC and Aeromar is in memory only), might as well have something hubbing around. It would create more jobs and if flashy advertisement of some of the DR's attraction (Colonial Zone, Altos de Chavon, Punta Cana beach, etc) are to be placed in the waiting area where the travelers in transition will be waiting for their transfer flight, that might create more interest for people to visit the DR.
It would also have been nice if a particular cruiseship company (European or where ever since there is no Dominican cruiseline company, is there?) to use one of the DR's ports as their home base.
Its just to increase the job supply, especially now that the free trade deal has been signed. Alot of agricultural job positions are going to go up in smoke due to cheaper imports.