We investigate the observational signatures associated with one of the proposed formation scenario for the recently discovered highly eccentric binary millisecond pulsar (MSP) PSR J1903+0327 in the galactic plane. The scenario requires that the MSP to be part of a hierarchical triple (HT), consisting of inner and outer binaries, experiencing the Kozai resonance. Numerical modelling of a bound point-mass HT, while incorporating the effects due to the quadrupolar interactions between the binary orbits and dominant contributions to the general relativistic periastron precession in the inner binary, reveals that, at the present epoch, the orbital eccentricity of the binary MSP should decrease for reasonable ranges in the HT parameters. The estimated decrements in the orbital eccentricity of the inner binary are few parts in 105, substantially higher than the reported accuracies in the estimation of the orbital eccentricity of the binary MSP, while employing various general relativistic timing models for isolated binary pulsars. For wide ranges in the allowed orbital parameters, the estimated rate of change in the eccentricity of the inner binary is orders of magnitude higher than the value recently measured by the pulsar timing analysis. Therefore, we rule out the scenario that the MSP is part of an HT undergoing the Kozai oscillations. The origin of this system in a typical globular cluster is also shown to be less likely than inferred in the discovery paper.