Do pure copper banana plugs make a difference in the quality of the speaker sound.

These are the desirable things in a speaker wire/connectors:

Must have low resistance so as to not increase the output impedance of the amp. You get that by using better and thicker conductors. Copper is fantastic. So, the purer the copper, the better the conductance. Having said that, no need to be ridiculous either. 99.99% of the people wont be able to tell the difference between 99% pure copper
and 99.9999% pure copper. Not worth the extra which only a very sensitive measuring device can notice.

Lower capacitance. Higher capacitance will impede hi frequencies. But then again, you
will not notice it in a few nano farads.

Lower inductance. Do not coil your wire, run it straight. Increased inductance may affect the rise time of your signal due to an inductor resisting the rate of change of current thru it.  Again, a few nano henries will not be noticed.

A perfectly good pure copper speaker wire of about 12 gauge can easily be bought for about $50. No need to spend any more, unless you want to run miles of it.

Low mass gold plated Z plugs.

Very tight fitting for maximum contact area. You can stack them into each other for jumper cables. They are not expensive.

Contact enhancers worth doing get a graphene one if you can it does make a difference. Dampen with fo.q. ta32 tape.

I wonder if they have done significant blind testing?

I would also be curious to know if I were blind tested to compare speaker cables if I would hear a significant difference?  I doubt someone would sit down to listen to a system and say this sounds like you are using Tera Labs or Kimber Cable.  I do think buying a decent set of cables does make sense, but not spending more than $1,000.  However, $1,000 is a lot of money.  The system should I guess cost at least $10,000 to warrant the expense.

Banana plugs are great for experimenters and folks who make a lot of changes, but they don't offer much contact area with the barrel they fit in to. You want maximum contact area. After all, there are two ends to the wire and the net effect of both connections must be considered. While I use many banana plugs and buy dozens every few months, I know spades or bare wire will give me a better connection. Remember, bare wire will squash down and fit the contacting surfaces very well. Copper is rather soft and will flow over time, loosening the connection. (That's why there are electrical fires in old houses.) Tighten them up every year or so. Spades seem to offer a good connection, but how do they attach to the actual wire? You have two connections on each end! The wire to the spade, and the spade to the speaker terminal (not to mention the terminal to the lead that actually goes to the actual speaker!). So, considering there are two connections inside the speaker "box," it is best to use bare wire and tighten the connecting mechanism really tight. The "tinning" you hear or read about is just to keep the many strands of wire in many types of cable from separating as the connections are tightened. A good idea. Use "silver solder."

I tried many different connections, but by far the most natural and real sounding speaker cable connector is the ETI Research pure copper spade. I always solder and use Wondersolder with very good results.

These ETI bare copper spades are better sounding than Furutech gold plated FP-201, even when you solder them instead of clamping with the screws.

I don’t like “squeezing” a wire into a connection ( unless it is a thick solid core like AWG 16 or more). The thin wires will be squeezed and this is limiting the “electron flow” since the surface is damaged. 
And please DO NOT TIN ( solder) bare ends and put them into a screwed connection. This will not give a solid connection as the tinning makes the cable very soft and is flowing under the pressure of the screw and being a loose connection.

I purchase the ETI spades from Hi-Fi-collective.uk, as it is half the price compared to VH Audio.Hope this helps to answer your question.