If the installation is assigned to the computer itself the program will be installed the next time it starts; you'll have to manually restart the server if there isn't some auto-restart mechanism.
If the program can not be installed without asking the questions, you wont be able to install it via GPO. You can initially test this by running
msiexec /qb /i installer.msi; if it installs you should be fine; otherwise it will fail. Depending on the program you might be able to get around this by specifying properties for the installer.
When manually run properties are specified in the form
msiexec /i installer.msi property=value and you can specify multiple properties. Check out the http://AppDeploy.com website for your app, it might have the information you need (if your app requires these properties).
You might also be able to create an Installer Transform (MST) that changes how the installer works slightly, thus allowing the program to be deployed. The usual tool to use is MS's Orca, which is part of the Platform SDK (IIRC). There are other tools available. The AppDeploy website might have info about writing an MST for your app; otherwise you'd have to learn Orca enough to fumble through it (hit-and-miss).
Rarely, the app vendor will publish information on how to write MSTs or Properties=Value pairs. (I love those vendors that do, makes my life a lot easier, especially with complex apps).
I'm looking around for a walkthrough, but not finding much. The basic publishing process in a GPO is pretty straight forward, the greatest difficulty is getting the MSI/MST files in order first.