Push mode means, as you wrote, that the clients are constantly connected to the Manager and then they download the definition as soon as they are published by the Manager.
Pull mode means that the clients poll the Manager at a regular time, then the downloading of contents will be on the first heartbeat after the publication of them in the Manager. Usually a heartbeat around 30-60 minutes is good.
Then, you don't need the LiveUpdate Administrator if the clients, in any communication mode, are able to connect to the Manager.
If the clients are not able to connect the Manager then you can allow them to download the definitions from the Symantec's servers instead of managing a LiveUpdate Administrator in your own.
You can use the Location Awareness in this way, for example:
Group: Laptops
Location1: Default (in the company)
Criteria: the client is able to connect to the Manager
LU policy: use the Manager
Location2: Out of the company
Criteria: the client is not able to connect to the Manager
LU policy: use the Symantec's LU servers