Is QOS traffic shaping necessary or worth it if your bandwidth is more than enough to handle it?

Here is my scenario I am running into. We live stream video to uStream and the connection is glitchy at best.

We have a Gigabit up and down fiber internet connection from Centurylink. Speedtest confirms the speed and connection are good.

The computer pushing the stream is a 1 year old iMac on a gig ethernet connection to a Cisco 2960 which then trunks over to a 3750 and then finally to our 4506 and Fortinet 600D firewall. All devices are connected over a gig interface.

at our peak during the live stream I only see around 200mb on the upload side of my interface from 4506 to firewall for internet traffic so we have tons of bandwidth available yet we still have this bad connection with uStream.

The stream is only around 20Mb and most of the time we have around 800Mb free on upload. Is there any reason to still do some traffic shaping to give the stream priority on the link?

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Cheers,
Chris