The negatively charged nitrogen-vacancy center (NV⁻) in diamond is a versatile platform for quantum magnetometry under ambient conditions. Recently, laser threshold magnetometry (LTM) has been proposed as a means to significantly enhance the sensitivity of NV-based magnetometers by incorporating a diamond hosting NV⁻ centers within a laser cavity and operating near threshold. While demonstrations have validated the concept, practical implementations remain technically demanding, requiring high pump powers and precise alignment of free-space cavities. It remains unclear whether the benefits of operating near threshold will outpace increased laser noise. In this work, we integrate an NV-diamond with a high NV⁻ content into a compact external cavity diode laser and demonstrate singlet infrared absorption optically detected magnetic resonance (ODMR). We report a five-fold enhancement in the ODMR contrast by operating near the laser threshold. However, the magnetic-field sensitivity is a factor of two worse near threshold (17 nT/√Hz) than when operating far above threshold (7.6 nT/√Hz). Consequently, on this platform, near-threshold operation currently yields a net negative effect on sensitivity because the threshold-enhanced laser noise outweighs the threshold-enhanced contrast. These results demonstrate that managing this contrast-noise trade-off is a critical challenge that must be addressed to realize the potential benefits of laser threshold magnetometry.