Chaining a non-Apple display (via a HDMI->Tb cable) to a (as yet unbought) Thunderbolt display on a MacBook Air (purchased Feb 2014): Workable?

The MacBook Air was bought in Feb 2014 and currently works with the aforementioned display via a HDMI->Tb cable.

This is what I get from the "system report" on my MacBook Air.

Model Name: MacBook Air
Model Identifier: MacBookAir6,2
Processor Name: Intel Core i7
Processor Speed: 1.7 GHz
Number of Processors: 1
Total Number of Cores: 2
L2 Cache (per Core): 256 KB
L3 Cache: 4 MB
Memory: 8 GB
Boot ROM Version: MBA61.0099.B21
SMC Version (system): 2.13f15
Serial Number (system): ---
Hardware UUID: ---

Thunderbolt Bus:

Vendor Name: Apple Inc.
Device Name: MacBook Air
UID: ---
Route String: 0
Firmware Version: 23.6
Domain UUID: ---

Apple Thunderbolt Display (27" flat panel)

Apple Thunderbolt Display (27" flat panel)

Product No Longer Available

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