If you block iexplore.exe (internet explorer) but you block aol.exe you won't be able to get on the internet with internet explorer. You will be able to access from Opera or netscape or something
IF you're not using AOL as an ISP
If you're using AOL as an ISP then yes it has to have access to the internet.
Yes a good firewall will block access just as it says it will. You just have to learn about dependancies.
For instance if you use crazybrowser or Avant browser and you block iexplore.exe you probably won't be able to use the internet because they both rely on internet exploder for internet usage, just as AOL does.
Once youget the applications setup to what you want and don't want to access the network then it does as you say. It pops up when there is something wrong.
It just takes time to train the firewall to your purposes.
There are firewalls that you can setup that don't rely on application level security but instead a lower level. Say open port 80. This will allow all access to port 80 no matter its source. This isn't so secure because MANY applications can use port 80 for inet access.
For your own PC a personal firewall works best. I don't like zonealarm myself but thats just my preference (I like Sygate better, but again you'll need to train it to your requirements)
I don't allow iexplore automatic access, I require it to request permission to access... iexplore is many times used by spyware for inet access.
you can go to
http://grc.com/default.htm to test your firewall software.