That's why you test - so you know whether or not something works. Additionally, there are significantly more important factors to consider than whether or a particular OS runs your application.
As a business owner with a process that has worked for X>0 years, unless there is a very compelling reason to do so, you don't want to risk disrupting your business with an upgrade of any core piece, especially the operating system.
Testing is fine and dandy, and breaks are acceptable in some circles, but in mission critical situations you can't be as frivolous.
There are reasons why you would want to upgrade, security, forward-compatibility, and product support. Since XP is becoming completely unsupported in a year, that's a very compelling reason.
Your last sentence doesn't really make any sense. If you're testing thoroughly you shouldn't run into any issues that are completely breaking.
That's why you test - so you know whether or not something works. Additionally, there are significantly more important factors to consider than whether or a particular OS runs your application.