In recent years, there exist human products designed using processes that model or mimic evolutionary processes, such as genetic algorithms. An example of this is the layout of integrated circuits.
I have to doubt that even Dawkins would argue that an integrated circuit ,designed in part using genetic algorithms, is a device that "only has the illusion of having been designed for a purpose". IMO Dawkins and his ilk go beyond the purely scientific in making such statements about biostructures.
If by "naturalistic processes" we include the "evolutionary algorithms" of nature, which are of course still ill-understood in total, one can make no scientific statement that there is, or is not, an underlying purpose reflected in these algorithms.
The question of "purpose" is simply not a scientific question.
On the other hand the hardcore ID advocates, IMO, err in denying the power of nature's evolutionary algorithms to generate design, and are revealing a theological bias of their own in so doing. They seem to think divine action is limited to using human engineering techniques of the 1940s.