The answer is positive and this is not difficult. The boundary of the Mandelbrot set is the set of $J$-instability. Every point $c_0$ of this set is a limit of $c_n$ such that $z\mapsto z^2+c_n$ has a superattracting cycle.
Ref. M. Lyubich, Some typical properties of the dynamics of rational mappings, English transl.: Russian Math surveys, 38, 1983.