Differential Gene Expression after batch correction with DESC?

I recently performed batch effect correction on single cell RNA-seq data with DESC.

www.nature.com/articles/s41467-020-15851-3#Sec11

eleozzr.github.io/desc/

The batch corrected clustering and dimensional reduction worked well but I would like to determine differentially expressed genes between cell populations from two different batches.

I don’t think DESC returns an adjusted gene expression matrix and the algorithm is innately tied to clustering, so is it possible to perform differential gene expression analysis on DESC batch corrected data/values?

My data is from a disease study and was processed over several months, so, unfortunately, the batches are more or less completely confounded with the biological conditions. As a result, I don’t think I can use any of the more “traditional” methods of batch correction (like MNN) which return a corrected expression matrix.

Once again, my question/problem is, whether it is possible to do DGE analysis subsequent to DESC batch correction.