The problems are that to live together as non-marrieds is also forbidden according to the Torah [albeit a lesser sin that adultery]. Another problem is גניבת דעת - misleading another person. An additional problem is that if they find out that they were fooled it will be a chilul Hashem. Also, if the Rav is being paid for this he will be receiving money for services not rendered. Also, the eventuality of infidelity is not 100 percent whereas the sin of living together without being married that he wants to cause them to commit [to save them from a greater sin] IS 100 percent so maybe it's better to hope they don't sin later and to conduct a proper marriage now.
Also - I don't like shtick.... [but then again I wasn't asked and maybe he is saving the woman from a חיוב מיתה].
See the surprising conclusion in the שו"ת תשובות והנהגות ח"ד סי' רפט [the only teshuva I ever recall seeing of Rav Shternbuch where he quotes a Rebbe from YU].