I used to sell air purifiers. Without researching the specific unit you mentioned, the basic info on all air purifiers is:
An ionizer will only knock the smoke out of the air, but it won't kill the odor. (also knocks dust and other things out of the air).
Something that puts out ozone will kill the odor. Ozone gets into things and chemically alters them. You can literally soak a rag in ammonia and hold it in front of a larger ozone generator for a few seconds and then smell th rag, it will have been reduced the basic equivalent of water.
In small quantities, ozone is harmless.
in medium quantities, ozone can be annoying.
In large amounts, ozone can be a little harmful, but you'll be very annoyed with it and even get a slight headache long before it reaches harmful levels, so don't be worried about that.
IF the unit puts out enough ozone, it should work very well to kill odors in the car. I'm sure its a very low power unit, so it would need a little bit of time to build up and become effective...... and if you chain smoke in the car, it might get overwhelmed. (maybe just get a second one then). but for the everday or average smoke, it should work.
EDIT: I just looked at the unit, it makes ozone, looks like it would work fairly well. REMEMBER, ozone is a compound that has to come in contact with the odor to work... so if you hide it under the seat with no airflow... well you get the idea, not gonna work