Yes. You should be able to bind the stackpanel's IsEnabled to your button's Visibility property. However, you need a converter. WPF comes with a BooleanToVisibilityConverter class that should do the job.
<Window
x:Class="WpfApplication1.Window1"
xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml">
<Window.Resources>
<BooleanToVisibilityConverter x:Key="BooleanToVisibilityConverter"/>
</Window.Resources>
<StackPanel>
<ToggleButton x:Name="toggleButton" Content="Toggle"/>
<TextBlock
Text="Some text"
Visibility="{Binding IsChecked, ElementName=toggleButton, Converter={StaticResource BooleanToVisibilityConverter}}"/>
</StackPanel>
</Window>
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