Hi,
Yes. Until the files are downloaded on WSUS server, the updates will not be available to clients.
By default, WSUS uses BITS service to download the files in background without impacting the network usage of other applications on the machine. Hence the downloads can be slow depending on the usage of network.
If you wish to speed up the downloads, you can let WSUS use all the available bandwidth for downloads by setting a confiugration option in the database - BitsDownloadPriorityForeground to 1.
Please see the article
http://support.microsoft.com/kb/922330for more information about the commands to set the option.
Thanks
Sudheer GN [MSFT]