My experience is as follows.
If the task is scheduled (prior to 4:30AM in your case) and the machine runs it's 4:30AM policy update, the end user should see the packages in the Portal.
If the task is scheduled after the machine runs it's policy update then the end user would not see the package in the portal unless they clicked on the "check for Additional Software" button (which triggers a policy update).
I'm not sure if there is more to this but this is was I observed.
So if I set the agent to run the policy more than once a day then the portal should come back up when the policies are ran the second time? Is this how you see it working or am I missing something?
If your goal is to keep the portal as upto date as possible then yes or simply tell your users to click on the "Check for additional software" if they do not see something they are expecting to have.
However the portal is best used to allow the end user to have control over the installation, if you simply want to software to install use "required installation".
Perhaps I'm missing something here?
Is the desired behavior to have the Software Deployment Portal automatically popup for the user when an installation is available?