I do not have any experience with such a device, but my best guess is that it would not work.
The adapter that you linked is designed to support a printer, and it comes with printer driver software to emulate the parallel port over USB. Application software that is intended to create printed output writes that output to the printer driver software, which provides a standard interface for handling printers. [Actually, the application software likely writes its printer output to a "print spooler" (software) that queues up print jobs so that they can be handled one at a time, and then the print spooler writes its output to the printer driver software interface.]
When using the parallel printer port to control a CNC driver, it is extremely unlikely that your controller software will be using printer driver software to control the parallel port, nor will it be sending its output to a print spooler. Rather, your controller software will almost certainly be writing directly to the hardware of the parallel port. It is therefore extremely unlikely that your controller software would be able to work with that USB to parallel port adapter as an alternative to directly controlling the parallel port.