Oracle complexity of a problem in the Counting Hierarchy
Yes. Each time your $\sf NP$ machine want to query the $\sf PosSLP$ oracle, simply simulate the polynomial time oracle Turing machine underlying the inclusion $\sf PosSLP \subseteq {P}^{{PP}^{PP^{PP}}}$, passing its oracle queries to the $\sf {PP}^{PP^{PP}}$ oracle.