Can I use (interact with) Siri without light the screen?
No.  This is not possible.  There are no configurable options to diable Siri screen dialogs.

I don't want to turn on the screen, because I don't need to read the response, I only need to hear it.

Siri (and Siri's developers) can't predict when you're going to read the screen or when you're only going to want to hear it. So, it is unlikely that this will change; Siri responds with both visual and auditory queues.