Today I added a Western Digital WDBABT0010HBK-NESN ("My Book AV DVR Expander", 1TB eSATA) to a FIOS STB (Cisco CHS 435HDC). I connected the devices with everything powered down, then plugged in the drive, waited a few seconds for it to spin up, and then powered on the STB. No messages or prompts appeared on the STB, and going thru the menus, it was apparent that the STB did not recognize that it had an external drive connected.
I tried a few different things to try and prompt the STB to recognize the drive. Finally, I had success by disconnecting the signal cable and plugging it back in when both the drive and the STB were powered on. The STB displayed a message about the external drive (forget exactly what it was), something about confirming its use. After that it seemed to work fine. Both the internal drive and the external drive appeared in the Capacity page, for example.
So, it seems that one has to plug in the external drive while the STB is powered on. That was counter-intuitive to me, but I did some googling and apparently hot-plugging is OK with eSATA. Verizon recommends ejecting the external drive before disconnecting it.