You are correct that there is/was a script called "Deploy Live Connect" to help pre-load components to the endpoints, but if you are using 6.2 and have installed the KLC Connection Relay Improvement Update you don't need to run the "Deploy Live Connect" script.
I remember seeing somewhere a post on creating a scheduled script to download and install the latest live connect plugin to endpoints, so that when you go to use it, you're not blindsided by having to re-install it. I know I should be able to find it, and frankly I haven't looked very deeply just yet. I will in the next couple days, but I thought I'd just ask to see if someone had quick access to a post or instructions, etc...
Then why do I have to wait 10 - 20 minutes sometimes the first time I try to connect via LiveConnect, when the agent has been installed all day long, and has been rebooted.