Short answer yes a USB serial port should work.
Slightly longer answer... there is a lot of manufactures and drivers out there, you may find that some USB-Serial adapters will work with your product and some wont... It all depends on how closely they follow the specifications (and which ones) for serial ports.
Where I used to work they had one specific brand/model they bought as they knew it worked with the hardware... sorry but I don't recall the brand ... Parallel port USB adapters don't play well with CNC machines because of timing issues, but the serial lines are usually used for sending/receiving DATA and not individual timed BIT control.
And USB is a Universal Serial Bus ... still serial data, but more overhead for multiple device addressing and higher speed capabilities.