The sequential ordering of different monomers within synthetic copolymers is remarkably difficult to control. Our understanding of the determinants of and variations within copolymer sequences, even in simple step-growth reactions, remains limited. In this work, we perform simulations on a generic model of irreversible step-growth copolymerization between two types of monomers, A and B, in solution. Our results demonstrate that relatively weak attractions among nascent oligomers can exert considerable influence over the sequential arrangement of monomers in the final set of copolymers, even when identical reaction barriers exist between all monomer pairs. The observed effects cannot be fully accounted for within conventional polymerization theories due to a breakdown in Flory's principle of equal reactivity that occurred in some cases. Nonetheless, these anomalous results can be readily explained by the Flory-Huggins theory, as a phase separation between A-rich and B-rich segments can emerge from and also be limited by the copolymerization process itself. This observation suggests that new routes for the one-pot synthesis of sequence-biased copolymers may be available through the coupling of step-growth copolymerizations and emergent phase separations.