It is possible to wordpress plugin or something like that that produces PDF files from the joined through the user form data, if this clicks the submit button?

I discovered these plug ins that permit posts be e-mailed or downloaded as pdf's.

http://wordpress.org/extend/plugins/tags/create-pdf

If you're flexible, It appears easy to programmatically create posts out of your form posted with a user, then produce a pdf of this publish. The posts which are produced in the form could be easily designated a specific category which isn't displayed on the website.

To programmatically create, update, and remove posts, begin to see the WordPress Function Reference, and particularly:

wp_insert_post wp update post wp delete post

A fast google search exhibits lots of methods to create pdf's with php. Some hard, some less hard. I found this class that might get you started: "FPDF"

I've not done an thorough search from the Wordpress-plug ins, but from so far as I will tell the reply is no. Obviously, it might be easy to create this type of wordpress plugin on your own nevertheless the server hosting Wordpress will have to possess the proper libraries installed to ensure that the wordpress plugin to become helpful.