No and yes. You *do* have to "go there" to the script or html page, but you don't have to display the new URL to the user.
mod_rewrite can't "call" a script per-se; it is an in-line function in the server file lookup process for purposes of this discussion, so once it exits, it exits.
I'd suggest you call a script to do your counter function, and then have that script load a page or whatever you want to do afterward. You can use mod_rewrite to change the request for any page on your site into a request for the script, and then pass the originally-requested page to that script as a query string. After the script completes its function, it can then look at the query string and load the requested page for the user.
The above is still a bit general because I'm not sure I completely understood your question.