Can a voltage source have 0 power
... a voltage source with 0 current through it. Will the power of that source be 0 according to the formula P=V*i? 


Yes, the power supplied from the source is zero if the current drawn is zero.


  Is there a reason to use such a source if it neither provides nor receives energy?


Is there a reason to have a battery in my torch / flashlight if it's switched off? Yes, of course. It's there when it's needed.

I suspect that you have some idealised circuit in a homework problem and that the voltage source is in place to add a little confusion.