This is solely in control of the Senate and under whatever rules they choose to impose.
Do you think Ford has a right of appeal if she disagrees with one of Grassley's decisions?
They may try to mirror some of the conventions of criminal proceedings if they think it helps politically but that's all show.
But the legal jeopardy under oath is real. That is why Kavenaugh will be afforded the right of hearing his accuser before he has to respond.