A central question in graphene chemistry is to what extent chemical modification can control an electronically accessible band gap in monolayer and bilayer graphene (MLG and BLG). Density functional theory predicts gaps in covalently functionalized graphene as high as 2 eV, while this approach neglects the fact that lattice symmetry breaking occurs over only a prescribed radius of nanometer dimension, which we label the S-region. Therefore, high chemical conversion is central to observing this band gap in transport. We use an electrochemical approach involving phenyl-diazonium salts to systematically probe electronic modification in MLG and BLG with increasing functionalization for the first time, obtaining the highest conversions values to date. We find that both MLG and BLG retain their relatively high conductivity after functionalization even at high conversion, as mobility losses are offset by increases in carrier concentration. For MLG, we find that band gap opening as measured during transport is linearly increased with respect to the ID/IG ratio, but remains below 0.1 meV in magnitude for SiO2 supported graphene. The largest transport band gap obtained in a suspended, highly functionalized (ID/IG = 4.5) graphene is about 1 meV, lower than our theoretical predictions considering the quantum interference effect between two neighboring S-regions and attributed to its population with mid-gap states. On the other hand, heavily functionalized BLG (ID/IG = 1.8) still retains its signature dual-gated band gap opening due to electric-field symmetry breaking. We find a notable asymmetric deflection of the CNP under positive bias which increases the apparent on/off current ratio by 50%, suggesting that synergy between symmetry breaking, disorder, and quantum interference may allow the observation of new transistor phenomena. These important observations set definitive limits on the extent to which chemical modification can control graphene electronically.