Yes, that is correct.
Not putting an expires part in will create a session cookie, whether it is created in JavaScript or on the server.
See https://stackoverflow.com/a/532660/1901857
For the use case in the question (no server side code), sessionStorage is a simpler solution. But sessionStorage is client only, so would not work if you need to access the stored value on the server (e.g. user logins etc.)