Exactly. You could just have php use the template and fill it in with your new data, then save it as another name.
There may be fancy functions to help you with this. I know there is when writting to a PDF or FDF file.
I know you can do this with Excel, so chances are you can do it with word: You could have php create a word object in your browser window if you choose to print it, and just display the newly created word object to your browser window for printing, or save it and email the saved file.