Well, they would have had a better chance, yes, but the lack of immigration from Europe was not what ending up dooming them. Precipitously-based littoral nations are going to have trouble surviving, especially when established on a semi-hostile population (more hostile than not, likely by this point) and surrounded on all sides by a united foe. Once the states can be sustained in depth (at least up to the desert of northern Arabia) then you have a better chance for longer-term survival.
You're putting the cart before the horse here.