The short answer is no, because the Jobe server is stateless, unless you deliberately change it. For example, you could turn on a database or set up a directory with write access to everyone, although I strongly advise against either of those.
The ploy we use if we want to link randomised questions within a quiz is to use one of the fields of the STUDENT variable (see here: https://github.com/trampgeek/moodle-qtype_coderunner#the-twig-student-variable) as a random number seed. For example you might ask the student to write a make_file(username) function that uses the given username as a random number seed and writes a randomised to the current working directory. Then you can ask them to re-use that same function in later questions that require that file.