Answer:
It depends, there are different types of people that use it.
~ The Fan - Usually this is the type that wants to see his/her favorite characters together. Or add in a character of their own into a story such as Harry Potter.
~ Aspiring Writer - Someone who wants to work in writing one day, but is using the site to improve his/her writing ability through constructive criticism. This person may also be considered a fan of a certain book or movie and that is what they will write on.
It all boils down to the person using the site and how often they use it. Some people that use the site will constantly be obsessed with getting reviews on their story. Or they will be obsessed with reading about their favorite pairings (Ex: Harry/Hermione). Fanfiction is just a way to pass the time, but some people do take it way to seriously.
So yes you could say it is addictive for some people.