Technically vibrato is going in and out of "tune."
But that is controlled, and I think that is the key to approaching the question.
If it's deliberate, creating some intended effect, it seems like a valid musical choice.
All kinds of slides, half-sung notes, etc. are used by singers and add life to a performance. By comparison when I hear a very "clean" performance of a song that it well known with a "messy" performance, it's the messy performance that is more expressive.
There is another specific case to keep in mind and that is the blues derived singing of a minor third over a major chord. Ex. singing an
F natural over a
D major chord which containers the
F# major third. By one standard that is horribly out of tune. By another standard - a bluesy standard - it's a gritty, dirty sound that is desirable.
Your "out of tune" stuff may be working according to a different aesthetic standard than something like... Taylor Swift, etc.
A funny anecdote: recently I went to a high school musical. The male lead sang out of tune the whole night! I mean clearly out of tune. At first it was strange. I kept thinking "how did this guy get the part?" After a while I didn't care and - in a strange way - it made the character endearing. He sang with such feeling (but out of tune) and in the end he brought home the part. (No, it wasn't my kid.)