Not quite. He came up in August 2006 and per Baseball Reference had accumulated 9 years, 41 days (9.041 years) of service time prior to the start of this season. He's added 58 days this year through today, putting him at 9.099 years. A season is considered 180 days, so come August 21 or so, he will reach the 10-5 mark.
That being said, given the way the Sox are going, he's not going anywhere this season.