Well, don't confuse background with project script. A project script can be used in both foreground (events) and background. Script modules are a way to avoid repeating oneself in code--not a control over how they are executed. Based on your description, I would certainly move that task to a function run asynchronously, and a project script is a good place to put such a function.
This sort of stuff is enough of a minefield that I created a number of wrapper functions to help, to be installed as a shared or global script. You might find this topic helpful: