Documentation for limma-voom analysis of RNA-seq data uses eBayes to perform pairwise differential expression tests. For more complex experimental designs, would it be reasonable to use edgeR's GLM method to call DE genes from dge objects containing voom transformed counts?

LImma can already accomadate any design matrix that edgeR can. It definitely doesn't make sense to use edgeR on voom-transformed counts, because edgeR models values on a raw count scale, and voom performs a transformation to logCPM.