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

The best connector is no connector, if your binding posts can handle that.

Yep, it seems the quality of the connectors is much more important than the cable between them.  If you calculate the right gauge, any cable will do. But the terminus is the thing. I run the cables all the way to the driver and solder the connection - the advantages of building your own. Soldered banana plugs the other end so they can be easily cleaned. 

Fact Check @ eric_squires, Gold is malleable / ductile by comparison. 
Copper, Silver, and Gold - Hard to Soft
As @cakids (and others) pointed out can be an effective plating element and conductivity is another matter.

I've posted this before in other threads and it looks like it's needed here;
http://www.tempoelectric.com/Wire_and_Cable_Facts.pdf

It seems using any kind of connector degrades the signal.

All the best,
Nonoise

@nonoise

this is why I suggest low mass, crimped banana connectors with Acoustic Revive contact enhancer. Replicating the force of crimping is near impossible on any normal binding post on bare wire and increasing connectivity of the imperfect banana surface is mandatory. On bare multi-strand wire the likelyhood of breaking wires is high, surface contact is low. On single strand wire chances are that in a bare connection the contact surface is even lower. Soldering adds resistance, no matter how good the solder.

Great reference article, btw