Certainly if we consider a single electron it will create a magnetic field associated with its movement. I don't like the words "couple with" because that suggests some special effect associated with the combined fields. Its field will add vectorally and temporally to the static field from the current loop. The current loop would see the temporal change as an induced voltage impulse of one polarity as the electron approaches and of opposite polarity as it recedes. Because of the sudden acceleration the approach velocity is less than the receding velocity so the two impulses have different magnitudes and widths. But the exchange of energy with the loop's current source is zero, it gains as much energy from one pulse as it loses from the other pulse. Of course we don't have single electrons, we have a current stream of zillions of electrons so those impulses all cancel out and we don't need to consider them. We have constant current arriving and leaving the acceleration point so the magnetic fields from those trajectories is constant. It is only the radiation from the accelerating region that is "seen" by the current loop. Of interest is just what is that radiation? You can argue that over the small accelerating region the current is constant because the changing density of electrons negates the effect of increased velocity, so there is no magnetic impulse to create an induction E field, hence there is no radiation. That is certainly a possibility. But my gut feeling is that there is a radiation E field there and that is what we are looking for.
Smudge
While the electron is accelerating, the E field is timedependent. If this Efield is also perpendicular to a steady magnetic field, then you have the necessary elements for a mode of induction predicted in Willie Johnson's Gyroscopic Force Theory. He is a member here, but has not been around since he last spoke with you about inner space, and something about a resistance of 30 ohms. He went and wrote a book based on the 30 ohms, titles "The Sagitta Key". The equation for this GFT induction is tExB=qr. He uses quaternions extensively, but his explanation of this equation is simple and we discussed it months ago on this forum. A timedependent electric field, perpendicular to a static magnetic field, will induce a current in a conductor. The units for qr are Coulombmeter, same as for the dipole moment. My take on that is that there is a change in density of the dipoles in the conductor.
