Will Splinter Twin and Combat Celebrant provide an indeterminant number of combat phases?
Yes, you can have an infinite amount of combat phases with Combat Celebrant and Splinter Twin.

As long as you are exerting a new splinter twin copied Combat Celebrant each time, your enchanted Combat Celebrant will be untapped and able to create a new token. This is covered in the gatherer rulings on Combat Celebrant:


  If you exert multiple Combat Celebrants in one combat phase, you’ll have that many additional combat phases, but all of your creatures are untapped only during the current combat phase. You’ll need to exert the Combat Celebrants one at a time, in multiple combat phases, to untap your attacking creatures and attack with them in each combat step.