The existence of an intergalactic globular cluster population in the Coma cluster of galaxies has been tested using surface brightness fluctuations. The main result is that the intergalactic globular cluster surface density (NIGC) does not correlate with the distance to the center of Coma and hence with the environment. Furthermore, comparing these results with different Coma mass distribution model predictions, it is suggested that NIGC must in fact be zero all over Coma. On the other hand, the results for NIGC and the faint end of the galaxy number counts (beyond mR=23.5) are connected. So NIGC=0 settles the slope of this function, which turns out to be γ=0.36+/-0.01 down to mR=26.5. The fact that NIGC=0 all over Coma suggests that globular clusters were formed only, or almost only, from protogalactic clouds. None, or perhaps very few, could have formed in isolated regions. It also seems inappropriate to advocate a relationship between intergalactic globular clusters and dark matter distributions, although it is true that the relationship could still exist but not be strong enough to have been detected. Finally, since our conclusion is that intergalactic globular clusters do not exist in Coma, accretion of intergalactic globular clusters might not be significant in galaxy formation and evolutionary processes in the Coma galaxies.