Yes, this is possible through record types and page layouts.
To make this work, you will need at least two Opportunity record types, including one record type for closed/Won opportunities.
Create a workflow rule and field update to update the record type based on when the opportunity changes to closed/Wonwon.
ThenNext, create page layouts and use page layout assignments by record type to dictate when the button appears.
Mike GerholdGerholdt, aka button click admin extraordinaire, has written a blog post on extending this functionality throughout the sales process here: http://buttonclickadmin.com/monday-am-admin-the-goose-and-the-gander/