Of course it absolutely will work. If you install Java and Clojure on a flash drive, it will work just as if you installed it on a regular hard drive.
As this blog post recommends clj.bat up the clj.bat file:
@ECHO OFF java -cp clojure.jar clojure.lang.Repl
Just keep in mind that your parent laptop will not have any environment variables (e.g. PATH), so depending on where everything is located, you need to configure it to make sure java recognized and clojure.jar is on the way to the classes.
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