Updated: It can, indeed, work with the Duo Charger. You can flip the strap around so that the watch back is on the outside and then pull up a bit on the straps wear they are attached to the watch. The watch back will then lie flat on the charger and everything works just fine!
I took advantage of the trade-in offer and ordered the Galaxy 5 Watch Pro in grey. It came with the Charger Duo. However, because of the strap which comes with the grey version (which I like very much), it can't be fully opened without. This makes it impossible to use with Charger Duo. What's the point of offering a free charger that doesn't work with the phone? Fortunately, the magnetic charging pads that were included with the Galaxy 4 Classic appear to work, but, really! This doesn't seem to have been thought out well at all.