Yes, it's possible but it's pretty advanced and you should consider hiring a sysadmin to set it up for you. We've been doing that for the last five years on our site. When an order comes in overnight, it gets printed to our printer 2000 miles away. When we come in in the morning, there is a stack of invoices sitting on the printer.
You need to learn about CUPS and how to invoke the printer from a Unix command line. This involves adding the printer to the CUPS config and learning about the lp command in Unix. That's the hard part of the job. One you have that working, then you can use PHP to execute the lp command. If your form is just a bunch of fields, then you're going to need to format it into some standard format first like PDF, JPG, PNG, GIF, or even simply TXT.
Hire a developer. This is probably not a task for a beginner.