Is it important to filter out poor quality cells before performing an integration analysis on single cell RNA sequencing data?
It is absolutely necessary to remove low quality cells: In the case of CCA (and this applies to other "integration" or "data alignment" methods as well), one would need to use "anchors", basically same type/state/kind of cells from the samples to be "integrated" and are used to "align" the different samples. In a scenario where you have a set of cells whose distinguished feature is high mitochondrial content due to apoptosis irrespective of their origin (epithelial, T cell, ...) and such cells are picked up as so called anchors, the whole integration effort will be off. Even when not using integration methods, bad quality cells quite often form their own clusters (highly skewed biology) not contributing anything to analyses and are often removed at the downstream steps anyway.

And when it comes to published work, unfortunately it comes down to the backgrounds of the reviewers. I tend to think that there are way too many single cell studies than experts with required bioinformatics and statistics so that a thorough review can be conducted. And lack of a paragraph on QC does not mean no QC has been performed anyway.