Suppose I have some 'control' samples drawn from some unknown multivariate distribution, and I want to test the null hypothesis that a particular 'test' point was drawn from the same distribution. Would it be legitimate to fit the PDF for the 'control' sample using kernel density estimation, then evaluate it at my 'test' point and take this as my p-value?

Suppose I have some sample $X$ drawn from some unknown multivariate distribution $F(A,B)$, and I want to test the null hypothesis that a particular point $x$ was drawn from $F$. 

Would it be legitimate to fit the PDF for $F$ using kernel density estimation, then evaluate it at $x$ and take this as my p-value?

Likewise, if I'm interested in the conditional probability $p(x~|~A=a)$, could I basically use the same approach, but just evaluate the PDF conditioned on $A = a$?