First, the Thunderbolt display can only be used connected to
a Thunderbolt port an a Mac. No other connection is supported.
FWIW, I have booted Firewire drives connected to the Firewire
port on the Thunderbolt display so I don't see any reason why
a TB drive can't boot.
Does your external enclosure have two Thunderbolt ports? I have multiple TB LaCie drive connected but all have two TB ports and I use them between my Macbook Pro and my Thunderbolt Display (the display should always be at the end of the chain).
I really don't think that, if your enclosure has only one TB port, that you're going to be able to do what you want. You may want to look into an enclosure that has two Thunderbolt ports.