What Rob and Dale said. The enclosure really is not dust proof, it just reduces the dust a bit. If I am not mistaken, the Woodfast has ventilation slots.
Over time there will be some dust buildup inside of an ODP motor and that will reduce the cooling efficiency of the motor. ODP motors are really intended for use in a non-dusty environment and also they should be more or less open to free ambient air for adequate cooling.
Since you will be using this for inverter duty, there are some other motor parameters that are much more important than deciding between ODP and TEFC. These include insulation class and temperature rating.
Insulation class refers to the ability of the insulation of the motor windings to withstand high voltages without arcing between adjacent wires. This is a problem with motors used for inverter duty. Very high voltage switching transients are generated that can be well in excess of a thousand volts. The symptom of this kind of failure is a gradual decrease in performance over an extended time. Motor manufacturers have addressed this problem by designing motors that are rated for inverter duty that have heavier duty insulation that is able to withstand the voltage transients without breaking down the insulation. I would recommend trying to find a motor that has an insulation class of E or better (i.e., class F or G or H). Sometimes motors may be rated for inverter duty with an insulation rating lower than E. In those cases the manufacturer may have used high voltage varnish to encapsulate the windings which enables them to withstand higher voltages.
Temperature rating is very important for motors used in inverter duty. The reason is that at slow speeds, the motor is not getting adequate ventilation from its cooling fan. For this reason, having the motor in an enclosure is a bad idea because the motor will run much hotter than it would if sitting in open air. It would be a good idea to consider getting a motor with a built-in thermal overload switch (not a fuse, but a switch). Also closely monitor the motor temperature for a while to make sure that it is not running hot all of the time. Consider replacing the front panel of the motor enclosure with something that will allow more cooling air to the motor. Hardware cloth isn't very pretty, but it may be necessary if you find that the motor is cooking itself.
Unfortunately, you will find that motors designed for inverter duty cost somewhat more than general purpose single speed motors. Some woodturners decide to take a chance with the lower cost motors. How long they last is highly dependent up many factors such as the type of inverter, the speed and load, temperature, and phase of the moon which makes it impossible to quantify.