First of all one should define what illusion means.
a) obsolete : the action of deceiving
b) (1) : the state or fact of being intellectually deceived or misled : misapprehension
(2) : an instance of such deception
a) (1) : a misleading image presented to the vision
(2) : something that deceives or misleads intellectually
b) (1) : perception of something objectively existing in such a way as to cause misinterpretation of its actual nature
(2) : hallucination
(3) : a pattern capable of reversible perspective
If one uses the "deceptive" part of these definitions, the answer is yes, the classical world is an "illusion".
BUT, when one starts being philosophical about our perception of the world one should keep in mind that everything that defines our existence can then be called an illusion. All information we have about the world around us reaches us through successive levels of proxies.
By level of proxies for example: we observe the world through our five senses, they depend on a level of cells organized to send information and store it, and that level depends on the organization of atoms and molecules, which depends on the quantum mechanical substratum of protons and neutros, which protons and neutrons depend on the substratum of quarks.
Another example: when we walk, we sense the earth beneath our feet as solid. It is an illusion because it is composed by a level of atoms which are mostly empty space as far as mass goes, and those atoms are composed by protons and neutrons .....
Nevertheless we do manage to walk, and are sure we exist because we ride as a biological pattern supported by forces over a complex stratum also supported by forces we have studied utilizing all these "illusionary" levels;we have also acquired an understanding of this in depth.
This happens because, as Vladimir concisely says, the everyday world is emergent from the complex levels of matter and forces beneath the dimensions we can measure every day compatible with our size : millimeters or at most microns for length, seconds, or at most microseconds for time. It is when our focus goes to smaller dimensions that the concept of "illusion" pertains.