In the past five years, approximately one third of the 65 pulsars discovered by radio observations of Fermi unassociated sources are black widow pulsars (BWPs). BWPs are binary millisecond pulsars with companion masses ranging from 0.01-0.1 solar masses which often exhibit radio eclipses. The bloated companions in BWP systems exert small torques on the system causing the orbit to change on small but measurable time scales. Because adding parameters to a timing model reduces sensitivity to a gravitational wave (GW) signal, the need to fit many orbital frequency derivatives to the timing data is potentially problematic for using BWPs to detect GWs with pulsar timing arrays. Using simulated data with up to four orbital frequency derivatives, we show that fitting for orbital frequency derivatives absorbs less than 5% of the low frequency spectrum expected from a stochastic gravitational wave background signal. Furthermore, this result does not change with orbital period. Therefore, we suggest that if timing systematics can be accounted for by modeling orbital frequency derivatives and is not caused by spin frequency noise, pulsar timing array experiments should include BWPs in their arrays.