I used to be a pretty big follower of this theory, so - as it hasn't been done yet - I thought I'd copy/paste some of my notes in here.
I've never touched the manga, and the anime has made mistakes before, so there's always the possibility that I could be off on a detail or two. I don't count anything that happens in an AO episode to be canonical, much like the movies and OVAs. (I'm hoping that's an opinion shared by everyone here? I'm relatively new to the forums.)
I've edited my original notes here and there, both for for wiki links and clarity.
The first piece of evidence is simply an impression I've gotten as the series has progressed, and as such may or may not be accurate. That impression being that it seemed at the beginning of the series we would always see Kogoro wake up some time after the Sleeping Kogoro act was over, but we very rarely if ever get to see this after around the ~300 episode mark. Again, it could be coincidence, or it could be that Gosho just felt the gag was getting old, or any number of things, but I wanted to point that out first.
The first piece of solid evidence is in episode 355, when Conan shoots Kogoro with the sleeping dart and he doesn't fall asleep immediately. In fact, he even carries on a conversation about the case and has time to mention something about a "mosquito bite" before the anesthetic takes effect.
Afterwards there's an unusually large gap in the series where we don't see Sleeping Kogoro again that seems deliberate, like it's trying to wait for us to forget about the fact that Kogoro wasn't falling asleep immediately. The next time we get to see him darted (disregarding AO episodes and I think there was one time when he was darted off screen) is in episode 387.
And something very interesting happens in episode 387. Just before Conan can fire the sleeping dart, Kogoro yawns, drawing the attention of Takagi, Ran and Megure. When Kogoro asks them why they're all excited all of a sudden, the three go on to explain the process in which he typically becomes Sleeping Kogoro, and they go on to tell him examples of some of the sounds and faces he's made. Immediately after this, Conan hits him with the sleeping dart and Kogoro makes an unusually dramatic noise and face. (Though not so much so as to definitely be suspicious on its own.) Ran comments that the noise and face were exactly right. Kogoro staggers on his feet for a few seconds before Conan pushes a chair behind him, Kogoro's fall timed perfectly with the arrival of the chair. (Again, this has happened before, and isn't in and of itself suspicious.) Then, before the deduction can start, Megure comments that Kogoro's position is "rather exaggerated". A probably irrelevant side note would be that this is also the episode where Conan learns of the "Seven Children" song, an obviously important part in the Black Org. plot.
Then, in episode 581 (which oddly enough is a case where Black Org. agents are crawling around everywhere) there's not one, but three possible hints pointing towards this theory being true. 1) Not only does Kogoro wake up before Conan can finish his deductions, but Kogoro himself finishes them using the email he reserved from Bourbon. This means that he'd been awake long enough to have heard and replied to what was being talked about. 2) Immediately after this, he turns to Conan and asks him (DCTP subs) "So, what happened to the bombing case?" 3) A short while later while Kogoro's talking to reporters and the like, he uses a slightly altered version of Shinichi's catch phrase: (DCTP again) "There is only one truth, after all!" This, unlike the other two, feels more like a hint than anything.
That's pretty much it, though it's entirely possible that I've missed details here and there, or maybe even forgotten some. But let's keep in mind that while the series enjoys making Kogoro out to be an idiot, he is actually a fairly competent detective - at least, when he wants to be. Here's a list of cases he's solved on his own with little/no help from Conan, just to jog your memory. Let's also not forget that Kogoro was the very first person, even before Ran, to become suspicious of Conan's identity, all the way back in File 10, in Volume 2 of the manga. (Manga referenced because it wasn't animated until episode 38, for some reason.) He even commented that Conan (paraphrasing) "reminded him of someone he'd met a long time ago, when Ran was in Elementary school."