That depends on who you ask. Sure, it can work, and authors like Jack Kerouac made an entire career out of it. Some readers are going to swear that it is the most effective story telling technique. Personally, I can't stand it. Personally, I don't think it is very effective in telling a story either. I'm a logical and ordered thinker. I like knowing that "a" gets me to "b" which gets me to "c." I like my stories and plot lines to follow a similar pattern. I like being able to think "I know where this character is going with this line of thinking." Don't get me wrong, I like surprises, but stream of consciousness always makes me feel like I'm reading one giant convoluted mess.
I don't want to say that stream of consciousness is all bad though. I don't think it works well to tell a story, but I do think it works well to develop a character. Let me use "The Catcher in the Rye" as an example. The story itself is being narrated by Holden in stream of consciousness. He's all over the place. For example:
She wanted to dance everything. Up real close to, so I could smell her breath. She didn't smell bad or anything. Don't get me wrong, she just didn't smell quite right. I mean girls should smell a certain way-like baby powder, new clothes and perfume. Something that was girlish, y'know. Jean, I swear, smelled like a fruit salad or Old Spice. I hate Old Spice. I mean I like Jean fine, y'know. She's great, but I just couldn't smell her.
Christ, I must be nuts. All of a sudden I start to imagine myself as the old sailor in the Old Spice commercial. Right out there on the dance floor. I start to think about coming home from the sea and bringing in the duffel and that song. It must have been the goddammed saxophone because that goddam song is running through my head "Dum dum de dum dum, dum di de dum dum da di dum dum" I see myself coming home to this really cute girl and wearing a sailor suit or something. I'm crazy. I mean, I'm really nuts sometimes.
I've never liked Holden because I always wanted to grab him and scream "FOCUS!" at him. I think that was Salinger's goal. Without the stream of consciousness, Holden would not be Holden. I wouldn't have such strong feelings about him. I don't have strong feelings about the story at all, which is why I don't think the technique works for story telling. It does work great for character development though.