Probably not, although we can't really say. But the fact is, the policy of women and children first was not really the big hindrance to filling the lifeboats (and I'm not sure why you'd assume it was). The biggest reason lifeboats went down only partially filled is that passengers simply didn't believe the ship was sinking at first. While the Titanic wasn't actually widely touted as unsinkable, in the initial stages of the sinking the ship was still fairly level and it was freezing cold outside - people simply didn't want to trust their lives to a tiny lifeboat in the middle of the North Atlantic at night when there didn't seem to be any real reason to do so.

It's also important to remember that there wasn't actually a hard-and-fast policy of women and children going first. Joseph Bruce Ismay and Cosmo Duff Gordon didn't have to sneak onto boats by pretending to be women, despite rumors to the contrary: they were allowed to board by the crew. The fact is that "women and children first" was a principle favored by men in general at the time (as I refer to in this other answer of mine about popular views of the Titanic), and it was the men escorting women and children who generally insisted on the point. It was simply not honorable for a man, particularly a gentleman, to survive in a situation where his survival meant the death of a woman, particularly a lady, and/or a child. This is why Ismay, Duff Gordon, and other first-class male survivors faced so much public criticism and scorn once the survivors disembarked from the Carpathia - people, including and probably even mostly men, felt that they were taking up spaces that could have gone to ladies - and why they defended themselves by saying that there were no women or children in the vicinity when the lifeboat was being lowered and that, furthermore, the lifeboats they got into weren't full, so they weren't even taking up valuable real estate.