It would be very foolish to sign such an agreement. The only possible purpose for including a (totally false, according to your post) statement that the parties never lived together or consummated the marriage is to set the stage for an attempt at green card revocation on the grounds of marriage fraud. What other possible reason could there be for including such language? It is normally not required as grounds for divorce, and it seems unlikely that it would make much, if any, difference in financial settlement arrangments.
Normally, once one has received an unconditional (10-year) green card based on marriage, the green card is safe from attack, but not always. This could be one of those cases where losing a green card might be possible, no matter how many years one has been a permanent resident. There is no statute of limitations for revoking a green card if facts come to light later on showing that the green card was obtained by fraud.
Anyone who is unwise enough to sign such a statement should be prepared for an attempt by the spouse or her family to have his green card taken away. The attempt might even be successful. A good divorce lawyer should be able to help in negotiating a realistic separation or divorce agreement which does not contain blatant falsehoods about the marriage relationship or put anyone's green card in jeopardy.
The above is general information only, not legal advice, and does not create an attorney-client relationship.
Attorney at Law
New York NY