As the title says, are campaign drops affected by the rewards for the companions I'm fighting with at the time? For example, fighting the Canictonis in Southmarsh. If I used a Grouger that doesn't drop the same items, would I get any chance to drop Grouger items like dye and cotton? I've tried watching to find out myself but I've ADHD and watching the fights play out is akin to torture for me xD

No, drops only correspond to the enemies you defeat!