No. The cardboard and marbles are the substrate on which the program runs; one might as well argue for the self-awareness of the individual carbon atoms in your brain. The program can't run without some sort of substrate, but the substrate is inert without the appropriate program; it is the system as a whole which is self-aware.

Godel, escher, Bach by Douglas Hofstadter is a colorful, whimsical, yet rigorous treatment of this argument in book format.