Do speaker cables need a burn in period?

Possibly. Objectively, speaker drivers absolutely have been shown to measurably change until they break in. The resonant frequency drops during the first 48 hours of significant play. 

How much this happens is very much driver dependent. Some may do so very little, some a lot. I'm a big fan of Scanspeak, and their woofers and mids will definitely change until broken in. 

I've also had experience with capacitors in the crossover breaking in, but that's harder to prove. I'm convinced, but I don't care if you are. 

Best,

E

Towards the end of life the suspension in speaker drivers will deteriorate, but that is a decade away from first use. 

The break-in period is usually within first 48-72 hours of use, and designers take this into account, so for this period at least, performance will improve.