I'm looking if there is exist specific hardware implementation of the
K-NN (K nearest neighbors) algorithm that represent the
samples/training set in physical coordinates on silicon or board. The
distance between the samples will be measured by the time it takes to
the signals to propagate between the two samples.

About K-NN algorithm:
http://users.rowan.edu/~polikar/CLASSES/ECE555/Lecture3.pdf 
slide:49/59

More information about further research in this area:
http://iris.usc.edu/Vision-Notes/bibliography/pattern619.html

Valid answer will be: 
Yes + links or no + relevant and sufficient sites and key words you searched in.

Hi guynice,

   It is possible, But what I suggest you that why can?t you use
MATLAB VR (Virtual Reality)Or MATLAB simulink for simulation of KNN.
You can simulate complete environment and test your efficiency of your
KNN algorithm.

    Otherwise you want to test in real Environment I have Solution, To
explain it I need Diagrams and some clarification from you, If think I
can give you the solution then mail me at nayan.ambali@gmail.com ....

Regards
Nayan GA