I think it could be possible.
I was digging earlier on a relationship between Jim Acosta and Secretary Rene Alexander Acosta (Sec. of Labor). Both of their parents are immigrants from Cuba. Jim's parents settled in Virginia and Alex's parents settled in Miami.
I found an article from 2016 that Jim wrote regarding a trip he made to Cuba in 2009. In that article he stated that he stopped to visit his Aunt in Miami.
So, Alex's family and Jim's Aunt both in Miami seems to indicate a possible familial relationship. Jim as WH correspondent and Alex as Sec. of Labor, seems a bit too much of a coinkidink.
Sauce: https://www.cnn.com/2016/03/20/politics/obama-cuba-us-relations-journey/