It does help if the user has ever had any public channels. Nodes with public channels publish a network string in LN gossip, and depending on how the user set up their node, it is either a tor url or their ip address. If such a user then creates an invoice, anyone can look ip that user's network string.

As a result, if you have ever had any public channels, you are at risk of exposing your ip address via your invoices unless you run your node on tor. Running on tor thus sometimes helps your invoices hide information about your node -- specifically, its ip address.