No. It's just flat-out impossible. Lusitania and Mauretania were battling it out amongst each other, a sibling rivalry if you will, with Mauretania not only winning but holding it for 2 decades. Olympic, Titanic's mechanically identical sister, was in service during those 20 years and she never beat it. Simple fact is Mauretania was faster than Olympic could have hoped to be.

There is a possibility that they were trying to beat Olympic's crossing or otherwise arrive early. However, letters that have been uncovered between Ismay and his company seem to show that wasn't the case. Ismay is actually resisting his company's desire to speed up the voyage.

http://www.titanichistoricalsociety.org/articles/ismay.html

There was a site that actually had the letters on display. I'm looking for that right now.