No, it would not work. Booting time will fail.
No sure what is the purpose of installing on removeable drive? You may want to try those so call mini win 10 or win PE like Hiren, Medicat etc if using it just for recovery use.
I have Medicat, quite a useful tools as it has Win10, Linux and some other utilities boot from USB.
I installed Window10 on my USB3 SSD for quite some time already. So I can run my own windows on any Computer which can boot from USB, it is quite fast and you will not feel any differences when the OS is running on External SSD.
Just follow the instruction from Windows Control panel and Click "Windows To Go" to install the OS on USB SSD or USB TB.
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