Save PDF file using webform2pdf
No you cannot save it on the server. One way would be to create your own code to grab the pdf with a tool like cURL and save it to the server. You could trigger your code to run every time a webform is submitted throught Rules and Webform Rules. You could issue a feature request to the module developer in case he wants add this fuctionality.

There is also this module: Fill PDF that does what you require. It is quite harder to get it to work with Webforms since you need to build your own pdf form template.