If a petition to extend L1B status is timely filed, the foreign national generally falls into a period of authorized stay once the I-94 expires. During this time, s/he is technically out of status, but is permitted to remain in the U.S. while the case is being adjudicated (including time spent while the RFE is being reviewed.) If the petition is approved, the person returns to L-1 status. If it is denied, the person falls out of status and begins to accrue unlawful presence from the day after the denial onward.
Generally speaking, if an application to change to B status if filed while the person is in a period of authorized stay, USCIS will not approve the case. Further, filing such a case will not protect the person while it is pending.
That being said, so long the L-1 worker is complying with the terms and conditions of his status, he may remain in the U.S. while the petition is pending (even if wife's reason for staying is because she wants the child born in the U.S.)