It all depends upon the SATA controller and it's driver. If you have an Intel SATA controller, and your BIOS supports AHCI, you should be all set (assuming that you enabled AHCI). There is a freeware driver that you can try that may enable the hot-swap feature if it doesn't currently exist. You'll find it at: http://mysite.verizon.net/kaakoon/hotswap/index_enu.htm
I don't have any eSATA devices, so I have no experience with the above referenced software. Use at your own risk.
My eSata outlet are on the MB..I think it thinks my eSata Dock is a second internal HD
My SDock is a Lantec nextar, I have hasked for help, but they answered to check for myself ...
If you're running windows, sometimes it's best to open the "device manager" and highlight "disk drives". Right click and tell it to "scan for new hardware". This usually does the trick.