Are eSATA drives hot swappable?

Your SATA controller (probably integrated in the motherboard) may or may not support this feature. It's likely if you're dealing with a new motherboard that it does. Basically, older motherboards supported something call IDE emulation rather than using native SATA Advanced Host Controller Interface (which does support hot-swapping).

From the Wikipedia article on SATA:

All SATA devices support hotplugging. However, proper hotplug support requires the device be running in its native command mode not via IDE emulation, which requires AHCI (Advanced Host Controller Interface). Some of the earliest SATA host adapters were not capable of this and furthermore some older operating systems, such as Windows XP, do not directly support AHCI.

...

While the drivers included with Windows XP do not support AHCI, AHCI has been implemented by proprietary device drivers.

I had this problem also with my bump down drives. (Buy a new one, clone the old one to it, replace the old one with the new, put old drive in external enclosure, reformat and new outboard drive created...)
I have been use Uwe Sieber's USB Drive Letter Manager and his Drive Tools for "Safe Removal", Eject, ReMount and others..
When I had a similar problem with my eSATA drives, I dropped him a line. Uwe recommended Hot Swap! by Kazuyuki Nakayama. It does the trick and more. My XP SP3 box redetects the Hot Swapped drive at device power up, although there is a "Scan for Hardware Changes" that is the first entry on the tray icon context menu, I don't generally have to use it.
Hot Swap! will dismount almost anything.

One thing Hot Swap! does not do, (or I haven't RTFM enough) is to turn off the light on a USB stick the way "Safely Remove Hardware" does, but I've looked at open handles, device manager, and "My Computer" and once Hot Swap! says it is gone, it is.