Define an ideal motor as one that is 100% efficient. Then a real motor is an ideal motor wrapped in problems, like armature resistance, core losses, windage, friction, and other mechanical losses.
If \$k_m(i) = \frac{T_{out}}{i}\$ is the ideal motor's torque "constant" at any given current (I put "constant" in quotes, because here it depends on current), then by conservation of energy, it simply must be the reciprocal of the ideal motor's speed constant: \$\omega = \frac{V_a}{k_m(i)}\$. You can even, after an adventure in SI units, show that \$ \mathrm{\frac{N \cdot m}{A}} \$ has the same units as \$\mathrm{\frac{V \cdot s}{radians}}\$.
So it's certainly mathematically possible for the efficiency to be high at high currents, as long as the copper losses are low enough. If that's really true, I'd expect that a motor excited at a constant voltage would actually increase in speed at high torque.