Okay, I'm not Sean...
...and will never be able to ride like him, but I'll take a stab at answering your question.
Theoretically, clutchless upshifting will improve accelleration--if you do it right. There's less lag time for clutch work and engine RPM doesn't drop much. Motorcycles have a constant mesh transmission, so the upshift minus clutch won't do any damage--if you do it right. (I do not suggest clutchless downshifting.)
Now, "to do it right," all you have to do is unload the transmission for a split second by shutting the throttle ever-so-briefly. With a little bit of upward pressure on the shifter, it'll snick right into gear. Once you get good at it, if feels like one motion.
(Racebikes have quick shifters that cut engine spark briefly through a sensor wired to detect pressure on the shifter so the rider doesn't have to manually unload the tranny.)
Will it improve your street riding? I doubt it, but it's fun to do. On the track, it's preferred.
Now, I'm guessing that Sean uses the clutch between first and second gear (as I do) because most bikes prefer to be shifted with the clutch there; the difference in ratios between 1 & 2 are farther apart, making the 1-2 clutchless upshift kind of sloppy and herky-jerky.
Did I forget anything, Sean?