I am a big fan of scooters (currently owning five Vespas - four of which are classics, and one which is a twist and go 300cc SS Super Sport). But I also own a fully tourateched Dual Sport Motorcycle (BMW F650GS Dakar) and a full blood Enduro bike (Yamaha WR250F). I have previously owned a Sports Tourer (Honda CBR600F) and a coiuple of other bikes, and I have done my fair share of adventures with all. And the point that I am leading up to, is that my advise is rooted in personal experience with various types of rides, including twis and go scooters.
I think the major benefit riding a twist and go scooter is that they under most conditions are easy to ride and are very comfortable, especially if you invest in a large wind shield (it will slow you down, but you could have a smoke in the rain, riding full speed, without getting wet or cold, and you won't get tired from the wind noise). Where you with a motorcycle need to apply a bit of muscle, telepathy will do the same job on a scooter. If the road surfaces are good, I can ride more hours on a scooter than on any motorcycle I have ever ridden, and often cover as much, and sometimes even more distance, than on a motorcycle.
I would not have any major concerns doing an RTW on any scooter, new or old, twist and go or manual... except if I planned to take routes with extremely poor road surfaces... which I like to do. The small wheels and shock travel in particular will limit where you will want to go, especially when fully loaded. Although a scooter is capable to do a lot of things, it is not the same to say that it is suitable. Also, luggage carrying capabilities is also more cumbersome as there are no really good off the shelf solutions... and there are no solutions that will leave you nice and balanced (either too wide, to high and/or to far back)
Small alloy wheels, low ground clearance, short shock travel, low power to weight ratio (including rider and luggage), will leave you feeling less confident and happy where the riding gets tough or unpredictable. It may keep you from seeking some adventures that you would have sought out with something more suitable.
As for the displacement, I would not be concerned. I think you will only feel that this is a big sacrifice on high speed highways where everyone zooms by you.
My advise, unless you have a particular kinky fetish for your twist and go, is that you trade it in for something more suitable. If cost is an issue, and you like to ride something small and light, then something like the Yamaha WR250R is a great type of bike. Strengthen the rear sub frame, get a set of cheap soft saddle bags, a wind screen and a jerry can (or larger tank if you can), and you are ready for an RTW.
If you want to see scooters in some real hard core adventure action, please see the trailer from my last adventure (it is a production for TV which hopefully the producer will be able to sell off to some nutty channel):
Budapest to Bamako Official Trailer - YouTube