Can gene co-expression networks be used to help identify differentially expressed genes? In my RNAseq dataset of differentiated stem-cell lines, some samples have far fewer significantly differentially expressed genes than others. QC shows that this is because there are way fewer reads for one sample than the others.

Can gene co-expression networks be used to infer differential expression? For example, if certain genes just miss the cutoff q-value cutoff  If so, what papers have done so?
While you can use networks to find differentially expressed genes (see the WGCNA package, which does this) in my experience this ends up largely matching what you'd get using a traditional package with a looser threshold for significance. Given the time savings of traditional packages, there's rarely any gain to using networks (it won't hurt to try, just note that it'll take some time). If some very interesting genes are just above your significance threshold then change your threshold. You need to validate your findings in some way anyway, so your p-value threshold is partly just a way to protect you from wasting your time (but if background knowledge suggests that your time wouldn't be wasted...).