“Catholic leaders” are probably 99.9% Dem voters, so I would say, no, they’re not trying to promote the GOP in any way, shape or form. They’re trying to protect the Church.
I don’t think it’s 99.9%—but my guess is the great majority of bishops and priests vote Democrat. I don’t know if there is any solid evidence to draw general conclusions, just a lot of case-by-case instances where a given bishop or a given priest has let his leanings be obvious.