No, greater cross-breeding within society does not reduce the risks associated with children of an incestuous relationship.
Genes are paired with one coming from the father, the other from the mother. For a child of unrelated parents, a gene which would give rise to a weakness or defect usually has no effect, because the other in the pair is dominant over it. Problems arise with a child of an incestuous relationship because a defective gene of a grandparent could be passed via the father and via the mother making a pair formed of two identical, defective genes. With no “healthy” gene in the pair, the defect will be expressed. Whether the grandparent’s genes came from a small or wide pool is not relevant. The chances that a particular pair may be formed of two identical, defective genes is small but with so many pairs in DNA, the chance that are a few is significant.