Are UST tyres just as prone to punctures as running standard tyres with tubes?
No. Pinchflats are a thing of the past, and thorn/nail punctures seal themselves assuming you run sealant.
If you get a puncture on the trails is it just a case of removing the valve and popping a tube in?
No, not necessarily. If you use the ‘sticky string’ type repair kits you can seal the hole externally without having to unseatthe tyre from the rim, or even remove the wheel from the frame. You can be on your way within a few minutes.
You can still get pinchflats, though it is quite hard, you really have to slam it hard into something lumpy (I got one a couple of weeks ago). I’ve had about one or two punctures a year since I went tubeless, vs one or two a month before.
And being a cupid stunt I’m never carrying my sticky string which does work in most cases.
Tubeless really is The Future.