No. Stoicism to me is a system of not reacting emotionally, or getting caught up in emotions that comes with those reactions. That part shares something with Buddhism. But desire, which is forward looking/seeking is not a problem for a stoic. If what you desire does not come to you, then the Stoic and the Buddhist are fairly aligned, but the Buddhist goes further as in that quote, but trying to root out desires. I could imagine some Stoics seeing this as cowardly. A true Stoic can keep his or her desires AND STILL keep cool when disappointed or thwarted.
(I find both philosophies demand one be split against yourself, so they are not appealing to me personally, but for slightly different reasons.)
Granty, for the record that quote I attributed to Buddha was actually by Epictetus, a stoic. So...you might want to rethink your stance a little bit.
http://en.wikipedia.org/wiki/Stoicism (see quotes at bottom of page).
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