This paper evaluated the performance of an envelope enhancement (EE) algorithm subjectively by children with auditory processing disorder (APD), and objectively through computational models. Speech intelligibility data was collected from children with APD, for unprocessed and envelope-enhanced speech in the presence of stationary and non-stationary background noise at different signal to noise ratios (SNRs), both with and without noise reduction (NR) algorithms as a front-end to the EE algorithm. Furthermore, intrusive and non-intrusive objective speech intelligibility metrics were derived to predict the perceptual impact of this EE algorithm. Subjective data for stationary noise conditions revealed that the combination of NR and EE algorithms significantly improved the speech intelligibility scores at poor SNRs. In contrast, the same combination was ineffective in improving speech intelligibility in non-stationary noise conditions. Taken together, subjective results suggest that exaggerating the envelope cues improves speech identification scores for children with APD. However, the benefit obtained varies depending upon the type and level of the background noise. Both intrusive and non-intrusive objective speech intelligibility estimators exhibited good correlation with the subjective data, with the intrusive metric demonstrating better generalization capabilities. Implications of these results for hearing aid applications for children with APD is discussed.