Yes, a constantly accelerating charged particle does emit electromagnetic (EM) radiation. According to classical electromagnetism, an accelerating charged particle generates changing electric and magnetic fields around it. These changing fields propagate outward from the particle as electromagnetic waves, which are a form of electromagnetic radiation.
The emission of EM radiation is a consequence of Maxwell's equations, which describe the behavior of electric and magnetic fields. One of Maxwell's equations, known as the acceleration equation, states that a time-varying acceleration of an electric charge produces radiation. This phenomenon is often referred to as "acceleration radiation" or "bremsstrahlung" (German for "braking radiation").
The emitted radiation carries away energy from the particle, causing it to lose energy and decelerate. As a result, the particle's acceleration decreases over time, eventually leading to a constant velocity when the emitted radiation's energy loss is balanced by the applied force or acceleration.
It's worth noting that the amount and characteristics of the emitted radiation depend on factors such as the magnitude and direction of the acceleration, the charge of the particle, and its mass. In certain cases, such as when the acceleration is extremely small or when the particle is moving at relativistic speeds, the radiation emitted may be negligible or exhibit different properties due to relativistic effects.