Yes this is possible, try something like this:
# bookmarklet
<a href="javascript:var answer = prompt('What is your name?'); var head = document.getElementsByTagName('head')[0]; var script = document.createElement('script'); script.src = 'https://ajax.googleapis.com/ajax/libs/jquery/1.5.0/jquery.min.js'; head.appendChild(script); $.post('http://localhost/script.php', { name: answer });void 0;">prompt_and_post</a>
a more readable version:
var answer = prompt('What is your name?');
var head = document.getElementsByTagName('head')[0];
var script = document.createElement('script');
# load jquery
script.src = 'https://ajax.googleapis.com/ajax/libs/jquery/1.5.0/jquery.min.js';
head.appendChild(script);
# do a jquery post
$.post('http://localhost/script.php', { name: answer }); void 0;