New carbon monoxide (1-0) observations of 29 spiral galaxies are presented and combined with previously existing data for 74 galaxies in order to study the dependence of the average CO surface brightness on the spiral-arm class. The total sample shows no significant correlation between the CO surface brightness and the presence or absence of grand-design spiral structure. The observations imply that most stellar density waves do not significantly influence the average surface brightness of CO. This suggests that, if density waves trigger molecular cloud formation, then they either inhibit the other mechanisms of cloud formation to keep the total formation rate constant or they increase the visible disk area of the Galaxy to keep the average surface density of molecules approximately constant. If density waves do not significantly trigger molecular cloud formation, then the giant CO complexes observed in density-wave spiral arms are temporary conglomerates of smaller molecular clouds that formed independently of the wave. 55 references.