can you marry someone to get them legally into the US?

What if your family in the US were very close to another family in Africa. Let's say the dad of that family became very ill and died. Could someone in your US family marry the widow and bring everyone here? What if they had to get a bogus divorce from their American wife in order to do so, with the wife's consent, even at her request? Would the INS see through this hyper fast?