I do not believe they do for internal transactions and just for anytime they have to directly work with the etherium blockchain. It truly depends on how they make the sub chain work, for instance if they hold it under a single Etherium address and then have arbitrary coins to pass around then it will only have interaction with the etherium blockchain when someone cashes in or out. However there rises another problem which is that a system based upon the Etherium blockchain would run into the same eventual problem of too many transactions (especially with teleoperations) and would inevitably slow down rapidly from having too many transactions.

Every blockchain design comes with pros and cons and considering they have relatively little information on the structure of the blockchain, it would be stupid to make specific predictions. I will keep looking for it but I am not entering the contest. By the way, structure information is on pages 15 to page 18 and they do say that they use PoS not PoW and how transactions work (kindof) but it looks really... iffy.