Due to Gestalt Psychology, is the face an illusion? Gestalt Psychology maintains that we perceive a whole from parts, and that we fill in missing gaps.  The "whole" we perceive is more than the sum of parts we perceive - it also involves what our minds add in.

Given this, is the concept of a "face" a result of Gestalt psychology on our minds?  All that's on the face are eyes, ears, a mouth, and a nose.  Yet we combine all these parts (which objectively seem discrete from each other) and come up with the concept of a face (the "whole" in this example).

Is this kind of reasoning correct?
Dependent on your definition of an illusion, there is truth in your claim. 

A definition of an illusion is:


  [A] perception, as of visual stimuli (optical illusion) that represents what is perceived in a way different from the way it is in reality.


But then - what is reality? 

First off, Bach-y-Rita famously proclaimed, 'We don't see with our eyes, we see with our brains' (Abrams &amp; Winters, 2003). The reason he said that is that everything we perceive is generated within our brain; it's a synthesis of visual information (photons) flowing from the photoreceptors in the eye (rods &amp; cones) to the visual cortices. For instance, color and shape are mere reflections of brain activity. Colors do not exist - the brain synthesizes them by combining information from three classes of photoreceptors, each sensitive to another peak wavelength.

Secondly, the rabbit hole goes a lot deeper than the Gestalt Principles. The retinal image is actively completed by the brain (Ramachandran &amp; Ramachandran, 2005). There are two relatively large gaps in each of our retinae, namely the place where the optic nerve head leaves the retina, called the optic disc, or the blind spot. No sensations, and hence no conscious perceptions can be generated by these regions which are devoid of photoreceptors. Yet, we do not notice those gaps in the visual field, because the brain interpolates what it guesses might be there in the visual field and actively fills up the empty spaces in the conscious image.

As a consequence of this, people suffering from retinal degeneration might not even notice it, only when they start hitting street signs and bump stuff from the table. Even then, they often do not perceive the patchy dead regions in their retinae, instead, they know there must be a gap, because they are hitting things. The brain simply fills the gaps such that they are not noticeable in the visual percept. Nonetheless, entire road signs or entire crystal bowls or glasses on the table might be erased, as the brain simply extends the table image in our minds.      

References
- Abrams &amp; Winters, Discover, June 2003
- Ramachandran &amp; Ramachandran, Sci Am, April 2005