This article says yes.
I love me some Phil (despite his whining about his taxes, which may be justified if he played only in the UK -- http://www.forbes.com/sites/kurtbadenhausen/2013/07/22/phil-mickelson-wins-historic-british-open-and-incurs-61-tax-rate/ ).
But I have to say that right now he needs either 55 PGA tour wins or 2 more majors to have a top 10 career.
There are 13 guys with more major wins than Phil:
Phil's 42 total PGA victories does rank him 9th all-time (Snead, Tiger, Jack, Hogan, Palmer, Byron Nelson, Billy Casper, Walter Hagen, then Phil).
I don't think Phil has any claim whatsoever to be top 8, which I would say is:
That means Phil is clumped in with the next group of 8:
Watson, Palmer, Vardon, Trevino, Faldo, Phil, Byron Nelson, Billy Casper
Phil could be ranked as low as 16 or as high as 9. While Phil certainly has Arnold Palmer-like characteristics, it seems unfair to say he is better since Arnold has both more total victories and total majors. Tom Watson played a lot against Jack, and had only 3 fewer total victories and 3 more majors than Phil. So I think he needs to be top 10.
My analysis leaves Phil fighting hard for 11th with Trevino and Byron Nelson. I think Phil has had a better career than Faldo and I am unwilling to harken back to the dark days of golf and analyze Harry Vardon's greatness or lack thereof, so I will go with Phil there. Billy Casper had only 3 majors. I will go with Phil there, although I can see an argument the other way.
So how would I get Phil in the top 10 with 55 victories or 7 majors? Well, 55 wins would put Phil in the top 6 all-time in wins. 7 majors would move him into the top 10 in both major wins and total wins - it would be hard to say that he was not a top 10 player. Who would suffer the drop down to 11? I would say Tom Watson. He only had 39 total victories, so if Phil got to 55, he would dwarf Watson. At 7 majors, Phil would be only 1 behind Watson and have more total wins and 5 of Watson's 8 came at one major (the British).