I read somewhere, there was a guy who rode a 50cc model around the world. So anything is possible.
As for a carnet, it depends if those countries in question consider the bike to be a motor vehicle (I guess they would, but I'm not sure). The carnet does not have a lower limit on motor capacity. If the vehicle is a motor vehicle, then it needs a carnet. So, I guess check with the embassies of those countries.
In lieu of a carnet, you could pay the importation fees. I'm not sure if you'll get a refund. Again, check with the embassies. Some countries have high fees, like 110% of the bike's value, which in your case might be rather low, but here you're depending on the country's customs agents to assess the value, which may be higher than in your country, thus disadvantageous (this is one of the reasons for a carnet). So, if you get a refund when you leave the country and can live with being without potentially a few thousand dollars (I'm assuming here) for weeks or months, than I guess not having a carnet will work.
A carnet will cost you a few hundred dollars, so if you think you can get very low assessments of your bike at the border, then maybe not having a carnet is cheaper. Again, I'm making assumptions here. So, check if you need a carnet and what the importation fees are, and what the value of a new bike of yours is in the countries in question. Then you should have enough information to make a decision.