Would it be possible to connect via eSATA without using the AC adaptor?

If you have FireWire 800 connection, then you can plug in both the FireWire 800 and eSATA ports, turn on the power switch to utilize the FireWire 800 bus power, and do data transfers from the eSATA port for faster rates. However, it is not highly recommended because the power consumption for operating 2 hard disks may not be sufficient under FireWire 800 bus power while using esATA connection for other purposes. It is highly recommended to use the AC adapter whenever possible.