To my understanding (haven't yet read the paper, just the abstract) - most full-disk encryption schemes are implemented in OS as opposed to in-hardware, so if the attacker has deep access to the system they could probably find a way to write unencrypted data to disk? That may not work inside a VM though

It probably does. In the code example on page 5, disk activity is only generated to send a "1", while a "0" is encoded as a time with no disk activity.

They write only random data and discard any data they read, so FDE should not have any effect.