Not for most understandings of a "DC motor". Such motors are expected to be able to run in both directions depending on the polarity of the DC voltage. Obviously if this flips rapidly between positive and negative, the motor will heat up and possibly vibrate a bit, but it won't "run" as normally expected.
Some types of motors run fine from both DC and AC. These use a coil instead of permanent magnets to create the stator magnetic field. Since both the stator and rotor fields reverse with the polarity of the voltage, the torque is in the same direction either way. These types of motors will run from either DC or AC, but can only run in one direction.
