Answer
Yes, it is separable.
Work Step by Step
Since the logistic differential equation is given by
$$
\frac{d y}{d t}=k y\left(1-\frac{y}{A}\right)
$$
then it can written as follows
$$
\frac{d y}{k y\left(1-\frac{y}{A}\right)}=dt
$$
Thus, we see that it is separable.
