Its going to depend on the online ordering package you're using. If the orders aren't going through your POS, then the print job will have to come from somewhere else. You probably won't be able to use an existing Micros printer; their print jobs come from the Micros workstations.
The only way I can see using an existing printer is if you have IP printers. They may be able to accept a print job from a second source, but you'll need the drivers and some kind of software to format the print job.