Does sexual intercourse a marriage make? No. Sexual intercourse and a covenant relationship with God are two different things. It's a fine arrangement when they overlap, but they don't always have to. A man and a woman can be having sex without entering into a covenant relationship, and they can enter a covenant relationship without having sex.
Whether the two parties acknowledge it or not, union between the sexes pictures a spiritual truth. This truth (the two intersecting parts becoming one flesh) becomes illustrative only as long as the two parts are joined.