The long and complicated answer “is no, and this is why-”. HDMI cables supply a DIGITAL signal (as opposed to analogue). There are key differences between the two technologies.

I found an excellent explanation on ‘boardsus.playstation.com‘ (HERE)

Wires send electrical signals… Plain and simple.  Anything sent over a wire is ultimately just a voltage/current applied to that cable.  Let’s say we’re talking about an analog video signal that’s 1 volt peak to peak… In other words, measuring from the LOWEST voltage to the HIGHEST voltage will give a result of 1 volt… With an analog signal you have “slices” of time that are “lines” of signal… It’s too complex to go into here, but basically you have a “front porch” which is known as the “setup”… This is what helps your tv “lock onto” and sets the “black level” for the signal.  After that you’ve got each line of the image (455 half cycles per line).  Again I won’t go into how chrominance (color information) and luminance (picture or brightness information) is combined, separated, etc.. It’s too complex for this discussion, but irregardless, just know that following that porch you’ve got all the lines of the picture (and some that don’t show up on the picture… these carry closed captioning, test signals, etc…).

Analogue Signals: If you look at one VERY SMALL timeslice of the waveform of an ANALOGUE signal, the EXACT position of the form (i.e. what voltage is present) represents what information is at that position…
Because of this, it’s VERY EASY for other radiated signals to get “mixed in” with that information.  When this happens, the more “noise” you get mixed into the signal, the more degraded the picture will be… You’ll start to get snow, lines, weird colors, etc… Because “information” is getting into the waveform that doesn’t belong there…With digital however, (i.e. the signal sent over an HDMI cable), the information is encoded differently… At it’s lowest level, it’s nothing but a string of bits… In other words, each signal is either ON or OFF…  It doesn’t care if a particular timeslice is 4.323 volts or 4.927 volts… It’s just ON…  For each “slice” of the signal, the “bit” is either on (if the signal is high) or off (if it’s low)…

Now, for a slightly easier to understand analogy…
Think of it this way… Let’s say you have a ladder with 200 steps on it… An “analog” signal represent information by WHICH step the person is on at a certain time. As you move further and further away (get “noise or interference in the signal), it’s very easy to start making mistakes… For example, if the person is on the 101st step, you might say he’s on 102nd, or as you get further away, you might start making more and more mistakes… At some point you won’t know if the person is on the 13th step or the 50th step….
NOW… In a digital signal, we don’t care if he’s on the 13th or 14th or 15th step… All we care about is rather he’s at the TOP or the BOTTOM… So now, as we back you up further and further (introduce more noise), you might have no idea what STEP he’s on, but you’ll STILL be able to tell if he’s a “1″ or a “0″…
THIS is why digital signals aren’t affected by cheaper cables, etc… Now eventually if you keep moving further and further back, there may come a point where you can no longer tell if he’s up or down… But the good news is, digital signals don’t “guess”… If they SEE the signal, they work… If they DON’T, they DON’T.. LOL

So if anyone ever tells you they can “see the difference” between HDMI cables, etc… You can knowingly laugh to yourself and think about how much money the poor sole wasted on something that was pointless.
Now, I’ve seen others say that they make a difference in audio… ALL audio carried over HDMI is STILL in digital format… So again, since it’s a digital signal, it will not make ANY difference at all….