The extremely large number of unique polymer compositions that can be achieved through copolymerisation makes it an attractive strategy for tuning their optoelectronic properties. However, this same attribute also makes it challenging to explore the resulting property space and understand the range of properties that can be realised. In an effort to enable the rapid exploration of this space in the case of binary copolymers, we train a neural network using a tiered data generation strategy to accurately predict the optical and electronic properties of 350 000 binary copolymers that are, in principle, synthesizable from their dihalogen monomers via Yamamoto, or Suzuki-Miyaura and Stille coupling after one-step functionalisation. By extracting general features of this property space that would otherwise be obscured in smaller datasets, we identify simple models that effectively relate the properties of these copolymers to the homopolymers of their constituent monomers, and challenge common ideas behind copolymer design. We find that binary copolymerisation does not appear to allow access to regions of the optoelectronic property space that are not already sampled by the homopolymers, although it conceptually allows for more fine-grained property control. Using the large volume of data available, we test the hypothesis that copolymerisation of 'donor' and 'acceptor' monomers can result in copolymers with a lower optical gap than their related homopolymers. Overall, despite the prevalence of this concept in the literature, we observe that this phenomenon is relatively rare, and propose conditions that greatly enhance the likelihood of its experimental realisation. Finally, through a 'topographical' analysis of the co-polymer property space, we show how this large volume of data can be used to identify dominant monomers in specific regions of property space that may be amenable to a variety of applications, such as organic photovoltaics, light emitting diodes, and thermoelectrics.