Possibly yes. I've only ever heard of players being willing to take less. Here is a link to an article showing players from different sports who have taken pay cuts to stay with a team, or to be able to play one more year even if they might not be the player they used to be.
Here is another article from 2005 where Chipper Jones of the Atlanta Braves offered to take a pay cut so that the Braves would be able to keep Tim Hudson.
He was introduced to Jones, the Braves' highest paid player, who's owed $32 million over the next two seasons and has $15 million vesting clubs options in 2007 and 2008. He could restructure his contract to clear up funds for a Hudson offer.
"Maybe a little rebate so we can sign him," said Jones, the only non-catcher who showed up Wednesday, doing some hitting and pronouncing himself healthy.
"Whatever [it takes]," Jones said. "I'm game. I've made no bones about it - my family loves it here, and I love playing here. I've made sacrifices before, and I'm open to more if it'll help bring guys in or keep them. I want to win."
It is very uncommon that a player, especially one signed to a huge contract would ever take a pay cut to stay with a team, or be able to sign with a team who has a chance to go all the way. It happens quite a bit in basketball, with older players who want to win a ring(reference my first article).
Lester even went so far as to admit that he would take a pay cut in order to stay in Boston and help his team win a consecutive World Series title. His inspiration for being so outwardly willing to take less pay in order to remain on the team he loves comes partly from his teammate Dustin Pedroia, who decided to leave a larger offer to stay with the Red Sox. As much as I dislike this team and their recent success, it enthralls me to hear this kind of talk in the offseason.
Here is another quote from this article that shows Jon Lester's willingness to take a pay cut to stay with the Red Sox, just as Pedroia took a lesser offer from the Sox to stay.