Manufacturing of high-performance carbon nanotube (CNT)-based polymer composites has long been complicated by the difficulty of infiltrating the nanoporous network presented by continuous CNT materials; this can yield composites with heterogeneities that drastically worsen their mechanical properties. We show the synthesis of CNT-polyetherimide (PEI) composite yarns via in-situ interfacial polymerization (ISIP), which side-steps slow, viscous polymer transport by infiltrating and reacting monomer species in-situ via a rapid and scalable process. We demonstrate the ISIP technique on two distinct, industrially-produced CNT yarns, and identify processing parameters that achieve conformal polymer coatings, yielding statistically-significant increases to linear density-specific tensile properties. Using ISIP on pre-densified yarns results in composites with specific stiffness and tenacity of 142 N/tex and 2.2 N/tex, respectively. When ISIP is applied to lightly-processed, porous CNT yarn, the specific stiffness and tenacity reach up to 66 N/tex and 0.7 N/tex. The role of interfacial effects, particularly from amorphous carbon, on the composite properties is also explored. Finally, we demonstrate a prototype roll-to-roll ISIP apparatus which can process arbitrary lengths of yarn for continuous composite production.