Yes, but one usually refers to a relationship by the closest term. If someone is your spouse, your first cousin, and your fifth cousin twice removed – you refer to the person as a spouse.
In some American states, such marriages are prohibited (though I suspect the prohibition, left over from canon law, would be unconstitutional). Jewish law has no problem with it, though some geneticists might take issue (especially if the common ancestor, the grandparents of the couple, had any recessive traits that one wants to avoid, e.g. Tay-Sachs disease).