Supposedly, if it's a short distance, like 2 meters or less, it shouldn't. Also, on paper the way HDMI is supposed to account the digital packets sent and received it shouldn't.
If you are going to view 4k, you want a HDMI that says "high speed" and I believe 18g compatible.
Some years back when I first bought my processor, I bought a $40 I think Belkin HDMI. The audio wasn't right. I tried everything to cure it. I was about to take back the processor when I had an idea to try another cable. I bought a good quality Tributaries and it worked, problem solved. My vision, even then, wasn't good enough to tell reliably if any video benefit. I suspect if the audio was poor, the video probably was affected in some way.
I've also had HDMI cables, cheap ones, go bad. It made the picture go black intermittently. I thought the TV was messed up, come to find out problem cured after replacing the cable.
So I don't go crazy on cost, use mostly a mid price Tributaries. I'd rather spend the money than have issues I have to deal with.
Back to the processor for a moment, that $40 cable worked when I tried it from a BDP to TV in my daughter's room. So either the satellite receiver stream wasn't on par or maybe the Marantz demanded a certain quality signal. Not sure. But, I am admittedly one of the suckers that will spend for better HDMI. .
On longer runs where the signal is getting weak it's said to cause like white flecks to show on screen. If one goes bad, or, the run just too long, you'll just get a black screen.
If you have a shop you deal with they should be able to lend you something HDMI to see if you notice a difference. If you do a comparison I'd be interested in knowing what happens.