No, Ghostly Gaze does not work that way
The Eldritch Invocation Ghostly Gaze from Xanathar's is explicit in how it works:
As an action, you gain the ability to see through solid objects to a range of 30 feet. Within that range, you have darkvision if you don’t already have it. This special sight lasts for 1 minute or until your concentration ends (as if you were concentrating on a spell). During that time, you perceive objects as ghostly, transparent images.
Nowhere in that description does it grant you the ability to see in Darkness or to see Invisible Objects.
In fact, both of those already do have mechanical options available to do so: The Eldritch Invocation Devil's Sight is what allows you to see in magical darkness and the spell See Invisibility allows you to see invisible objects. The language in those mechanics specifically allows for those interactions while the language in Ghostly Gaze does not.
There is no reason to think that such language is implicitly added. Without calling out explicitly that Ghostly Gaze grants vision in magical darkness or the ability to see invisible objects, you can not just add those mechanics to it.