Well, not really IME.
My first thought is: well, then it's not really a major chord any more, is it?
But, you're just creating some unresolved tensions against the major tonality — I think it would depend on what (i) melodic lines you're creating, and the overall "shape" of the same (ii) if what you call a major tonality isn't really major at all, but is based on some kind of altered dominant or some mode from a lydian scale or...whatever it might be...could be a lot of things, that I personally don't think are really done any service by nitpicking about modes from the melodic or harmonic minor scales. But, rest assured, people have come up with all kinds of odd naming conventions.
If it's just including a raised nine against a dominant chord, or even a dominant chord with the major seventh as a (perhaps prominent, melodically) passing tone,, then it's really a blues thing: AFAIC, the blues tonality based on dominant chords isn't really explainable by common-practice-period harmony. But it's still a sound everyone is accustomed to, even though the tensions of the tritone in the dominant aren't what you'd expect from a "home key."
The short answer is: well, it just depends on what tensions against the major chord you're including, and if they're resolved, where they're going, where they're placed in the rhythmic scheme.
And the very short answer is: sure, it's common.
Topic: Minor scale over a major chord?