Will variables still work when a user leaves and then restarts the course?

Hello! I'm hoping someone wise can help me.

I've designed a course with a variable at the start which captures a user's name. I use this variable throughout the course to personalise it.

However, if the user leaves the course before the end, and is then brought back to the slide where they left the course (ie they are not reinputting their name), will the naming variable still work on later slides?

Thanks