First of all, you need to be careful when saying the train does not accelerate. In Physics, acceleration is the rate of change of velocity. As velocity is vector, if the velocity of the train changes direction, as it does on the curved portion of the track, then the velocity is changing over time (changing in direction). Therefore, there must be an acceleration to allow the velocity to change direction.
In circular motion at a constant speed (not velocity), this acceleration is called the centripetal acceleration, and its direction is always perpendicular to the velocity. As a result, the velocity only changes direction, but not magnitude (constant speed).
However, I assume that what you mean is that the train's engine is not contributing any change of speed.
If this is the case, we have two key forces to worry about: the centripetal force, which the rails exert on the wheels, and friction, which includes air resistance. The centripetal force causes the centripetal acceleration which, as said earlier, causes no change in speed.
However, the friction forces will generally act in the opposite direction as the train's velocity (its more complicated in reality). As a result the friction forces cause an acceleration that decreases the magnitude of velocity over time.
So, yes, the train will be slower after the curve due to friction. However, since there is always frictional forces, the train would slow down regardless of the presence of the curve anyways. Whether the curve causes any significant increase in frictional forces is more difficult to say, as that depends on the mechanisms of the wheels, and for simplified analysis, it could be ignored.