I have various Kindles including:
My Kindle Fire first model, second edition, WiFi - it can access any web site over wifi
My Kindle 4 WiFi and Kindle 5 WiFi can also access any site over wifi
My Kindle Paperwhite 3G can access Wikipedia.com over 3G. It asks for a WiFi connection to visit sites such as google.com This concurs with Nathan Osman's comment on ...
If you want to use the Kindle to read PDFs then the connectivity to the mobile network is not relevant once you have the PDF documents installed on the Kindle.
There are various ways documents reach a kindle, these include downloading them over WiFi and/or 3G connections. They can also be copied directly from a computer using a USB connection (using a USB ...
Using Calibre you could try :
Adding the book in the Calibre library
Sending the book to your Amazon email address (Right click on the book > Connect / Share)
Sending the book to your Kindle while it is connected to your computer (Right click on the book > Send to device)
Of course this requires some initial configuration (telling Calibre how to send email,...