question about litterbox use

I always wanted a dog, even though I am more of a cat person. But the third cat I adopted made me wonder about this:

If a dog has an "accident" inside the house, will a cat think it is OK to pee there and stop urinating in the litterbox?

I ask because I used to have a cat who sometimes peed on the floor.

I had a dog with many issues and never got housetraining or crate training.  It was just luck if he went outside.

My cats never picked up that habit.  I also cleaned up within minutes of accident happening.  I had a cat who was iffy with litter usage from the day I got her and a sick cat I held off neutering cause of his issues but they didn't seem to get worse cause of the dog.  Gracie peed otuside box even after dog was gone and Shawn stopped spraying within weeks of neuter.

I have never had any problems, if fact when my late lovely Fozzie was a pup and got caught short he would use the litterbox, so he copied the cats