The use of reversible addition-fragmentation chain transfer (RAFT)-assisted encapsulating emulsion polymerization (REEP) has been explored to prepare diverse types of colloidal stable core–shell nanostructures. A major field of application of such nanoparticles is in emergent nanomedicines, which require effective biofunctionalization strategies, in which their response to bioanalytes needs to be firstly assessed. Herein, functional core–shell nanostructures were prepared via REEP and click chemistry. Thus, following the REEP strategy, colloidal gold nanoparticles (Au NPs, d = 15 nm) were coated with a poly(ethylene glycol) methyl ether acrylate (PEGA) macroRAFT agent containing an azide (N3) group to afford N3–macroRAFT@Au NPs. Then, chain extension was carried out from the NPs surface via REEP, at 44 °C under monomer-starved conditions, to yield N3–copolymer@Au NPs–core–shell type structures. Biotin was anchored to N3–copolymer@Au NPs via click chemistry using an alkynated biotin to yield biofunctionalized Au nanostructures. The response of the ensuing biotin–copolymer@Au NPs to avidin was followed by visible spectroscopy, and the copolymer–biotin–avidin interaction was further studied using the Langmuir–Blodgett technique. This research demonstrates that REEP is a promising strategy to prepare robust functional core–shell plasmonic nanostructures for bioapplications. Although the presence of azide moieties requires the use of low polymerization temperature, the overall strategy allows the preparation of tailor-made plasmonic nanostructures for applications of biosensors based on responsive polymer shells, such as pH, temperature, and photoluminescence quenching. Moreover, the interaction of biotin with avidin proved to be time dependent.