We investigate theoretically the accuracy of an effective medium approximation in modeling localized surface plasmon resonance biosensors for the detection of biopolymer nucleation. Using boundary-element method simulations, we compute the extinction spectrum and spectral shift of a gold nanoparticle-biopolymer system in which biopolymers are treated as cylindrical rods and compare them with results from an extended Mie theory in which biopolymers are treated as an effective medium with a radially variable refractive index. Our results show that the effective medium approximation can be employed to predict the extinction spectrum and the spectral shift accurately. We also demonstrate that the approximation is effective even when there is only a single biopolymer on the nanoparticle, as long as its orientation relative to the incident wave is random, which is generally the case in solution-based localized surface plasmon resonance biosensing applications where the orientations of biomolecules relative to the incident light are not fixed, but change over time.