We are talking about 40k here, so dying will probably be the nice outcome you hope for...

Basically yes. It's pretty much a death sentence. The psyker could be saved if they get medical attention quickly enough, but it's pretty likely they gon' die.

In Dark Heresy 2e a 100 o Perils of the Warp table is instant death and you then roll to see if a DAEMON OF CHAOS shows up in the place you were standing on.

Not only is he yeeted screaming into the warp, but (depending on the edition) there's a good chance a daemon appears and kills what's left of the party