At closing, most mortgage lenders require that the borrowers sign an IRS form 4506 which gives them the right to obtain a copy of the borrower's income tax form. Mortgage lenders DO contact the IRS routinely as part of a good quality control program. It's a fraud prevention tool and they DO catch fraudsters using this method.
I strongly advise against falsifying tax forms used in a mortgage application. Though it is rare for the mortgage underwriter to contact the IRS prior to loan approval, they may flag a questionable file for quality control review immediately after closing. Either way, if you lie, you'll be caught. If they check prior to closing, you'll simply be denied. If they check AFTER closing, you may be prosecuted.