This depends entirely on what /subscribe is. If it's a single PHP file that handles the POST request then it should work fine. If it's a script that does other processing like an extension in Joomla then it probably won't work. All I can tell you is CB URLs will perform the POST for you, but where the receiving script accepts it or not is entirely different. The below URL would be more appropriate.
Code:
http://www.example.com/newsletter/subscribe.php
Then inside of subscribe.php it would handle the $_POST variables and add them to a newsletter.
It would seam your script isn't designed to be used as you're using it as the below also fails.
Code:
http://emarketing.ourblok.com/public/ocnaf02h9q/FbN/subscribe?sign_up_email_address=test@invalid.com
I recommend contacting the developers of your newsletter software on best approach for subscribing via URL.