User Synonyms and Notes are passed to the WK server immediately upon creation. But the WK server will not tell you what you just sent it until you complete the lesson quiz. It is write-only. The WK quiz page already did this for Notes. The WK server allows User Synonyms to be handled similarly. (Notes entered without this script on the lessons page expire/desync from the browser after 2-hours.)
You should be able to restart your browser. As long as it doesn't crash real bad and somehow corrupt or lose its html5 local storage data. Local data is only deleted after 180-days of no-viewing or upon lesson quiz completion.
The issue that much of this script handles is making the browser remember User Synonyms and Notes until you complete the lesson quiz. Even if you complete the lesson on another browser/device WK will still remember any User Synonyms or Notes you entered, but of course you won't be able to see them on any other browser/device until you complete the lesson quiz.
Short:
Yes. After quiz completion the User Synonyms and Notes will be visible on any browser.
You should be able to restart your browser. As long as it doesn't crash real bad and somehow corrupt or lose its html5 local storage data. Local data is only deleted after 180-days of no-viewing or upon lesson quiz completion.
The issue that much of this script handles is making the browser remember User Synonyms and Notes until you complete the lesson quiz. Even if you complete the lesson on another browser/device WK will still remember any User Synonyms or Notes you entered, but of course you won't be able to see them on any other browser/device until you complete the lesson quiz.
Short:
Yes. After quiz completion the User Synonyms and Notes will be visible on any browser.