Can you get Eevee without a national dex?

yes,but you have to trade with someone who has an evee or got to this girls house i think it is some where around the fighting area and talk to her.she will give you the eevee.

A DIFFERENT ANSWER (but this one is from Pinklovie123)

You have to beat the elite 4 (beat the game) and go to Bebe's house in hearthome city next to the Pokemon center. so the answer is no UNLESS you trade with someone as the person before me said.