If data
is not processed by the script running on the server receiving the HTTP Request, it is gone afterwards.
Your browser creates an HTTP request with the form data when you submit the form and sends it to the webserver specified in the form action. The webserver just knows how to handle the HTTP Request as such. Your PHP scripts have to know how to handle the data within the HTTP Request. HTTP is a stateless protocol, so there is nothing stored by the webserver.
Note: technically, when receiving GET requests with added params, you might find them in your webserver's access log, so they are stored, but it's not like you would reuse them from there.
Have a look at the Firefox addon Tamper Data to see what happens when you submit a form. If you want to use IE, try Fiddler.
As to whether you should use GET or POST as a form method, stick to the W3Cs recommendation:
1.3 Quick Checklist for Choosing HTTP GET or POST
* Use GET if:
o The interaction is more like a question (i.e., it is a safe
operation such as a query, read operation, or lookup).
* Use POST if:
o The interaction is more like an order, or
o The interaction changes the state of the resource in a way
that the user would perceive (e.g., a subscription to a service), or
o The user be held accountable for the results of the interaction.
However, before the final decision to
use HTTP GET or POST, please also
consider considerations for sensitive data and practical considerations.