Is the effect of hydroperoxyl radicals significant in the oxidation of organic compounds in the Fenton reaction? Why or why not?
The effect of the hydroperoxyl radical in the Fenton process can be largely ignored as the oxidising ability of the $\ce{^∙OOH}$ radical is not as effective as that of the hydroxyl radical.
According to Chang et al., the reaction rate coefficients of p-nitrophenol and $\ce{OH}$ and $\ce{HO2}$ were found to be $\pu{9.05 \times 10^6 M−1 s−1}$ and $\pu{1.50 \times 10^−6 M−1 s−1}$, respectively. Considering the orders of magnitude of these two rate coefficients, the reaction pathway involved the p-nitrophenol reaction with $\ce{^∙OOH}$ radicals can thus be neglected. This can therefore be extended to cover the oxidation of organic compounds by hydroperoxyl radicals through the Fenton process.
References

Chang, M., &amp; Chern, J. (2010). Decolorization of peach red azo
dye, HF6 by Fenton reaction: Initial rate analysis. Journal of the
Taiwan Institute of Chemical Engineers, 41(2), 221-228.
DOI: 10.1016/j.jtice.2009.08.009