By all means down load the trial and see what you can do with it!
Filemaker can do what you describe but you've already identified the key question: "( Whether it is in mine [ability] is another question )" Giving the trial version a try is the best way to find out if you have the time and ability to do what you want. Filemaker does come with an Invoicing starter solution you can look at for ideas. It does show a typical way to set up tables for products, invoices, etc though I think the inventory management features designed into it are dangerously flawed.
There are other invoicing templates and demo files you can take a look at. Here's one from another forum member, Comment, that you might want to look at: