As far as I have been able to ascertain (and believe me, I've been looking into this a lot recently), the engine in the current GasGas Randonne and the current 2012 model Scorpa TY125F (European model) is basically a [licenced?] copy of the original Yamaha 123cc engine you find in the TTR125 - ie. with an electric starter fitted - but it is not made by Yamaha at all.
However, I also understand that for 2013, GasGas at least will be offering the Randonne with a bigger bore (possibly an aftermarket kit, either dealer or factory fitted) which I imagine will be the same as the 163cc kit currently available for the existing/earlier Yamaha-engined Scorpa's, and which was basically the same as factory fitted to the TY-F200.
Now that, with it's street legal lights and an e-starter could very well make the perfect trail/play/dual-sport bike?
ps. Away from the factory/dealer offerings, another option is that in Europe at least, the Yamaha Trailway comes as a 125cc - so presumably they share the same bottom end/crankcases? (which I have yet to have confirmed) - If so, then I imagine fitting a TW200 or even a XT225 engine into the Scorpa or GasGas frame shouldn't be too much of a stretch - as long as the head/carb and ancillaries fit into the space available...