Is it allowed for one who is going through conversion to Kasher the kitchen before the conversion process is complete or is it a requirement that the conversion process be completed first?

In order to prepare him self for Jewish life and so he should know what kind of life style you are going to enter, a convert in process should have a Kosher kitchen. Nonetheless, since the conversion candidate is not yet Jewish, the kitchen will require Kashering after conversion and Toveling in Mikveh (without a Bracha) after Kashering.