Yeah, once the icons are there they aren't downloaded again unless
You recreate the docker.img (all of them need to download again)
You change the icon URL or the name of the template (only that icon will need to re-download)
You add another app (only it will need to download when going to the docker / dashboard tab)
To minimize problems with the tab, there is a timeout of 45 seconds (and a 15 second connection) to grab them. If it can't do it in that time then it aborts and next time you hit the docker tab it starts the process over again.
If you have in Settings - Notification Settings the check for docker updates disabled, then the OS will not check for updates.
However, whenever you go to the CA tab it will automatically start a background process to check all your installed apps (plugins and docker) for updates if it hasn't been already checked by CA within the last hour. This can be disabled in CA's settings.
Additionally (but not directly related), many plugins will also automatically check for updates available to them (in the background) whenever you hit their page or settings. This includes every single one of mine, UD, parity check tuning and one Dynamix branded) - IE: Whenever you go to Apps, it will always check for updates to itself. This behaviour cannot be disabled