In this study, we discuss the mechanisms behind changes in the conductivity, low-frequency noise, and surface morphology of biosensor chips based on graphene films on SiC substrates during the main stages of the creation of biosensors for detecting influenza viruses. The formation of phenylamine groups and a change in graphene nano-arrangement during functionalization causes an increase in defectiveness and conductivity. Functionalization leads to the formation of large hexagonal honeycomb-like defects up to 500 nm, the concentration of which is affected by the number of bilayer or multilayer inclusions in graphene. The chips fabricated allowed us to detect the influenza viruses in a concentration range of 10−16 g/mL to 10−10 g/mL in PBS (phosphate buffered saline). Atomic force microscopy (AFM) and scanning electron microscopy (SEM) revealed that these defects are responsible for the inhomogeneous aggregation of antibodies and influenza viruses over the functionalized graphene surface. Non-uniform aggregation is responsible for a weak non-linear logarithmic dependence of the biosensor response versus the virus concentration in PBS. This feature of graphene nano-arrangement affects the reliability of detection of extremely low virus concentrations at the early stages of disease.