Whether Esata connection works on external HDD like Seagate Barracuda

You would have to see how much they locked your bios or if you could flash to a differnt bios in order to get the boot device options in your bios, If your bios does allow you to choose your boot device then you should be able to, i know that you can use usb external devices as boot devices so i dont see why an esata cable would be any differnt the only problem is that it is a laptop and the bios options are very minimal