I want to put Alexa script on a page, but don't want the image to show up on the page, so if I put the Alexa script in a noscript tag will the Alexa script still work and and count my visitors coming to my page?
No. Code within a <noscript> block is only rendered if JavaScript is disabled. So browsers with JavaScript enabled will ignore any JavaScript in a <noscript> block.
i usually use <noscript> to show visitors a message to allow JavaScript in there browser so they can the content
My first question would be why do you want that malware garbage on a website in the first place? (I trust Alexa about as far as I could throw a PDP-8) Now that said, could you simply target the image with CSS, and absolute position it off the left side of the screen? left:-999em; good as always.