A problem with configuring the Firewall

Hello everyone. I have a question and will be grateful for your help.
when I decide to block a program from accessing the Internet does it knows it is blocked or it just sees no connection?
for example when I block my Player from accessing the Internet, It just works and just does not show advertisements, but I have another software that when it is not blocked, it works with no problem, but when I block it, it complains about not being able to connect to licence server. The interesting part is that when it is not blocked and I have no Internet connection it works well too! so it does not need a active connection.
I have no problem with letting it to access the Internet but I wonder what is going on.
thanks in advance.