Answer
No. It means that the negative terms in the numerator of $r=\frac{Σ(\frac{x_i-x ̅}{s_x})(\frac{y_i-y ̅}{s_y})}{n-1}$ prevail over the positive terms.
Work Step by Step
If a above-average value of X is associated with a below-average value of Y then the term in the numerator is negative.
If a above-average value of X is associated with a above-average value of Y then the term in the numerator is positive.
