Additive manufacturing and the development of electro-conductive nanocomposites via fused deposition modeling (FDM) are prominent research topics. Polymers such as polylactic acid (PLA), polyhydroxyalkanoates (PHAs), and PLA-PHA blends are commonly employed to this aim. To achieve electrical conductivity, fillers such as carbon nanotubes (CNTs) and carbon black are commonly incorporated. The analysis of the filaments prior to FDM is particularly relevant, as their electromechanical properties directly influence the final performance of FDM-manufactured parts. However, there is a notable lack of research addressing this aspect. This study focuses on manufacturing CNT/PLA and CNT/PLA-PHA conductive filaments and their electromechanical characterization. The filaments are produced by melt blending followed by extrusion and are used to fabricate monolayer tensile coupons via FDM in order to evaluate and compare their electromechanical behavior. The inclusion of CNTs led to a slight increase in tensile strength in both the filament and the FDM-manufactured specimens, but elongation at break decreased in the FDM coupons. A reduction of three orders of magnitude in the electrical conductivity of the filaments was observed after FDM, along with a significant change in their piezoresistive response. These findings indicate that, while the incorporation of CNTs may improve tensile strength, the FDM process reduces electrical conductivity and alters the material’s electromechanical sensitivity. Differential scanning calorimetry indicated polymer degradation, which is associated with thermal processes during extrusion and FDM. Such degradation resulted in a variation in the mechanical properties of the nanocomposites after FDM. These results underscore the importance of characterizing the polymeric filaments and the final FDM-manufactured parts to better understand and optimize the functional performance of conductive components produced by additive manufacturing.