Ebony fingerboards do make the guitar marginally brighter but you have to take into account what the rest of the guitar is made of, type of pickups etc.
A Les Paul Custom Classic - even with an ebony fingerboard - isn't going to be over bright, I wouldn't think.
If you've ever played a Yamaha SG 1000, 2000 or 3000 you'll get a good idea of what kind of tone a mahogany body - maple capped - ebony fingerboard is going to sound like, and I certainly wouldn't call them too bright sounding.
I believe that as a rule of thumb Alinco II magnet pickups are meant to be best for ebony fingerboards. Maybe someone can confirm this?
Will you have a chance to play the LP CC first?