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The transition to millimeter-wave and sub-THz frequency bands necessitates that the base-stations (BSs) utilize extra-large antenna arrays (ELAA) to compensate for the associated huge path-losses. However, when higher frequencies and shorter transmission distances are utilized, the spherical wave curvature can no longer be neglected. Hence, the ELAAbased wireless systems tend to operate primarily in the near-field. Thus, the far-field channel models used for near-field users may detrimentally affect wireless system designs and performance gains. To this end, we investigate the impact of mismatches between far-field and near-field channel models/precoders on the performance of ELAA-based integrated sensing and communication (ISAC). To this end, the achievable user rates are derived for the near-field. Two detectors for sensing a target are designed based on known/unknown BS/target channels. The performance of these detectors are investigated by deriving the probability of detection and probability of false-alarm. A transmit power optimization procedure is also proposed to maximize the minimum achievable user rate, while ensuring a power threshold for sensing. Numerical results are used to study the fundamental trade-off between the probability of detection and achievable rates for near-field ELAA-based ISAC. We unveil that ELAAs can be leveraged to improve the ISAC performance trade-offs.