Does form data still transfer if the input tag has no name?
The W3C specification, if I understand it correctly, mandates that every form input element has a name attribute specified. Otherwise that element will not be processed. Source
No.
I checked this in all browsers - the fields with empty/missing name are missing in POST/GET request from browser. It doesn't matter if they have or don't have id (my thought was that browsers might use id for name but no).