Well yes.
The order in which a browser reads CSS rules is, from Right to Left, so when you have a selector like .menu .submenu a.something, the browser would first look for all a.something elements in the DOM, then it's parent .submenu and then for parent .menu element.
So yes, having high specificity does slow down the rendering performance of the browser. Here's a good read on this topic.
Also, having hight specificity in CSS can lead to a lot of issues with maintainability. You should resort to using things like BEM that help with maintainability and keeping low specificity.