Anyone can raise a claim to injuries in civil court, to be sure. However entering into plea has consequences. The consequences are explained by courts to all defendants via colloquy. Waivers to process ARE part of that. Connecticut V. Doe. Where defendants lost 9-0. Those similarly situated were those who entered into plea and suffered conviction. All waived right to (more) process, including the option to advance appeals or contest usual civil action that may flow from the conviction.
We will see what the judge has to say in this case, my guess is most claims will be dismissed for lack of standing. Time will tell.