electromagnetism - Does a constantly accelerating charged particle emit EM radiation or not?

The Abraham-Lorentz force gives the recoil force, $\mathbf{F_{rad}}$, back on a charged particle $q$ when it emits electromagnetic radiation. It is given by:

$$\mathbf{F_{rad}} = \frac{q^2}{6\pi \epsilon_0 c^3}\mathbf{\dot{a}},$$

where $\mathbf{\dot{a}}$ is the rate of change of acceleration.

If a particle has a constant acceleration, $\mathbf{\dot{a}}=0$, then there is no reaction force acting on it. Therefore the particle does not lose energy.

Does this mean that a constantly accelerating charged particle does not emit electromagnetic radiation?