Dear Ashish,
As far as I know, the Class and Characteristics are kind of master data and thus it needs to be created in each system.
While executing the CLEO activity, I have faced the same issue but later it was discovered that, addition of Characteristics in class has to be performed in each system.
so answer to your doubt is that, it can not be transported. You need to do the same activity in each system.
Also, Import and export property will not help. It will just create a VATs but if the required class or characteristics is not exists then this process will not create it.
Please let me know if you have any more doubts, will be happy to answer it.
Thanking you,
Regards
Amol