Short answer: NO
Complex answer:
While he's not overrated per say, certain elements of his game are. People assume that Mata has a lot of goals and assists because he's a technical Spanish midget with the description "attacking midfielder". In truth, he scores and assists a lot because he's got what I like to call "a striker's awareness". He has the ability to be at the right place at the right time. He doesn't need to make defense-splitting passes or score classy goals. He's always there for the tap-in, whether he's last or second last on the ball. If you look at Mata's goals and assists so far, then you'll notice that few of them were results of impressive moves. His heel-kick assist to Januzaj was class, but other than that, his assists have been fairly simple passes, if I remember correctly. And then there's his set-pieces. The fact that he's good at set-pieces gives his game a whole new dimension.
Is Mata a better playmaker than the likes of Silva, Özil and yes, even Kagawa? In my opinion: no. In fact, he's most definitely not!
But Mata has something that these other players don't have, and that is ruthless effectivity. He's not the type of player to turn games around on a bad day, but when we don't suck(which we really should aspire to, being United and all), he's almost guaranteed to either score or assist. And that is valuable to have, regardless. In fact, that's the only reason we've let Rooney play in the AM position, despite being a crap AM.
Well, now we've got Mata, who's arguably just as effective as Rooney and has good technique! Rooney's "goals and assist guarantee" is pretty much rendered useless in the AM position now. You could make the argument that Kagawa shouldn't be ahead of Rooney in the pecking order for the AM position, because of his lacking effectivity. With Mata, you can't. Any sensible coach should see this. As long as we have Mata(and Kagawa imo), then Rooney really has no business in the AM role.
Mata is a brilliant player, possibly world class. He pretty much offers 80% of what Rooney offers in terms of goals/assists, and 80% of what Kagawa offers in terms of playmaking. Combined it makes him unique. Kagawa is the better playmaker, but he needs a lot more playtime in order to reach his Dortmund form. And it's not even sure if he'll reach it. Might as well play him on the wing for a while. Rooney is the better goalscorer, but he has mediocre technique, creativity and passing.