Point of view distance is an important decision you need to make when planning out a book. Stream of consciousness is the shortest possible distance, even closer than first person where the narrator is choosing what words to share with the reader. In stream of consciousness, the reader sees everything that passes through the narrator's mind. It is brutally honest, or at least as honest as the narrator is able to be with himself.
Now add thriller...
Not the full form thriller genre which includes psychological terror, suspense and some of the best opportunities for "reader-knows-something-the-character-doesn't" anticipation available anywhere. Just the distilled essence of the thriller, the impending homicide from the point of view of the soon-to-be victim, the moment-to-moment shocked to be alive while bullets fly everywhere, stolen moments of urgency before an inevitable, unending darkness. Thrillers of this type are heavy on adrenaline, light on detail, and totally devoid of explanation or extrapolation.
Can it be done? Absolutely and to great affect. But think of it like painting in black, white and with maybe only a few shades of gray. You can do it, but you have to drastically limit your pallet. Only some paintings can be pulled off in that style... and the same goes for stories that can be stream of consciousness thrillers.
Choose your story carefully. It must not rely on intrigue or subtlety. Character development or relationships between your characters is not likely to be important to the story. It needs to be obvious in its content and its intent. If anything requires explanation for the reader to understand, then this approach to story telling is not appropriate to that tale. Rest is rust. Nowhere more than here is that sentiment true. If your character gets more than a moment of rest between terrors, the tension of the narrative will fall apart. In that moment, you, as author, will be called upon to fill in all the omitted details that the earlier high-energy scenes left out; and in the absence of descent character development, backstory and setup, answers for those omissions will come off as fabricated, convenient and unjustified. In the absence of proper story structure, your quite moments will want to become infodumps.
If you can stretch such writing into anything longer than a very short story, consider it a victory. This kind of high energy writing is brutal to character and author alike.