I mean, no, it doesn't really. You'd have to be remarkably poor at receiving a pitch to affect every pitch. What you're saying is that every single called pitch is the opposite call of what it should be solely based on the catcher's receiving.
Not the opposite call on every pitch, but it can have a total effect. I --HATE-- fidgeting catchers. Stop moving. You have plenty of reach without having to leap 3 feet outside to catch a ball which is aimed at the edge of the plate. Umpires hate them as well - nothing like setting up for a pitch and the catcher leaps outside leaving nothing between you and the pitcher throwing 60+ mph. That is not a way to make friends.
My DD's catcher has been NECC/Catching Camp trained and she is a total joy to watch receive. Our other catcher is a moving mess which is slowly being fixed but is an uphill battle because of how she was taught (but she has a cannon for an arm which is why they like her)
If you want to see bad cacthing, watch the College Baseball World Series. There are some terrible, terrible catchers on some of these teams.