Single output at amp, tri wire at speaker. Any benefit?

If speaker manufacturers didn't think it made a difference, they wouldn't bother providing separate inputs.
As millercarbon mentions, if you have the cable availabe, just try it out.

If you don't most cable companies will be able to make a cable that has one set of leads for the amp and 3 pairs of leads to go to each of the terminals.
Even if you still use jumpers, you will notice a difference when using different cables.
Bob

First try running the main cables to different terminals on the back of the speaker, with the jumpers adjusted accordingly.  You may find a difference with using the tweeter vs midrange vs woofer input as the one that directly receives the signal from your amp.

Thank you . Haha! The solutions proposed are so logical. Silly of me to not have tried those out first. 
I will do the binding post jump first. 

Cheers
Jag