Adding an extra 1ft to premium speaker cables

Yes, it would.

ozzy

A common dilemma. 

I have gotten stuck in this situation before. I am an audiophile, so the answer was easy, be financially irresponsible, and buy a new set of the correct length. Hence I have no experience. 

However, given my experience with cables, I have a guess. With lots of caveats. Adding an extra foot of less expensive (note I did not say cheap) would sound better, than say just a full run of low quality cable. I would put the less expensive stuff attached to the amp. Hopefully it is like one tier down of the same brand of cable... not a completely different brand of cable... or hanger wire or something, 

There are so many problems with my rational, they are hard to count. That’s my guess. 

Intuitively, one would think it will defeat the purpose. If the cheap cable was to take away anything, there would be no way to put it back. However, since you are dealing with cheap cable, it would not cost much to give it a try and revert back to the original state if things don’t pan out. 
Keep in mind that the term cheap has different meanings depending on how deep your pockets are. Have you considered Ali Express cables? They seem to be over performing their price. 

Don't do it ...

I am curious why "there’s no way to change it", in regard to your needing one more foot.

Perhaps there is a solution that you haven't considered.