The DataTemplate doesn't have a DataContext either. It's the element that the template gets applied to that has a DataContext. So in other words: Yes you can do this with ControlTemplate too.
You can bind to attributes and symbol properties like so (assuming a FontSize property on the symbol class and a "Title" attribute in the graphic):
<ControlTemplate>
<TextBlock FontSize="{Binding Symbol.FontSize}" Text="{Binding Attributes[Title]}" />
</ControlTemplate>