Short answer: yes.
How much of that was in my head? I don't know if I could quantify that.
My first cue was an entry-level McDermott, 20 oz. with a 13 mm shaft. I played with that thing for several years and was happy with it.
Then I bought my first Meucci, an 18.5 oz. 84-4 with something called a 'pro taper' shaft. Whatever. It immediately felt better in my hands, and I shot a little better, IMO. It seemed easier to produce draw (the only english I knew how to shoot at the time), and somehow more accurate.
These days I know that I shoot more precisely with a shaft that's somewhere between 12.25 and 12.75mm. The thinner shaft seems to allow me to aim more precisely than something fatter. My favorite cue has a 12.5 mm shaft, and I'm just more accurate all around with it than the few cues I have that have 13 mm shafts. Now, for most shots there's little difference; it's only when I need very precise aim that it's noticeable to me. Things like kick shots, longer caroms, offset combos, and very high-angle cut shots. Those shots just seem to be easier with a thinner shaft. YMMV.
As for magical cues, I only have one. It's a Meucci HP-3 that I won off a guy, brand-new. In fact, the match itself was kind of an accident, or magical. Won't bore everyone with the whole story, but I won it from a guy that I knew was a hustler, and much better than me, but on the rubber game, he miss-shot the 6 into the corner and it rattled instead of going down. The look on his face was utter shock. I ran my two strips, dropped the 8 and walked away with that cue.
In almost 15 years of playing with that cue I won some incredible games, had some ridiculous runs, made some magical shots. Like a fool I sold it about 8 years ago I think when I was having money problems.
Crazy thing was, the buddy I sold it to suddenly became a better shooter with it. His average win total went up about 20% year-to-year. He went from averaging just under one 8-ball run out per session to almost 6. He never took a lesson or got in more practice time.
I got lucky and bought it back from him last year. My game has improved since I started playing it again, and I've semi-retired my newest Peach, sold my Predator, and traded away a Joss.
The only problem is that the stick is old; I'm scared I'll accidentally break it somehow. First world problems, I know . . . but that stick is somehow magical.