I got my first puncture on my Schwalbe Pro One tubeless setup today. Naturally, it was freezing and raining.
I noticed the back wheel felt a bit soft, so I stopped and squeezed it. Sure enough, deffo losing/lost air. Rode on a bit, hoping it'd self-seal, like the theory says.
Five minutes later, had another squeeze. Seems stable. Whip out the pump, lash in some air, so it feels properly hard again (70 PSI? Hard to say in the rain etc., but certainly good to ride).
Four hours later (snow, slush, water, even the odd bit of tarmac), safely home. There is a nasty little cut in the tyre, but no air coming out at all.
While I'm at it - the tubeless do seem to be faster than my usual Conti GP4000sIIs. Certainly hitting a lot of strave PMs without obvious additional effort. The new tubeless wheels are 33mm rims (AL33s), and so a bit more aero, in theory than the 22mm climbing wheels I'd usually use (and also about 350g heavier). I can't see the rims making a big difference (happy to be corrected), so inclined to credit the tubeless.
Anyway, that's just for anyone considering going tubeless - all my experience (maybe 500km) to date is positive.