Yes essential oil diffusers do humidify the air somewhat and add some moisture to the air while putting the essential oils into the air.
However essential oil diffusers only humidify the air just a little bit and in small amounts unlike the regular humidifiers do.
If you're planning to humidify your room then you should use a regular humidifier along with the essential oil diffuser so that you get the benefits of the humidity in the air and the benefits of the essential oils in the air.
I use and love my essential oil diffuser and a regular humidifier when I need to add moisture to the air.
But when I don't need the moisture in the air I use only the essential oil diffuser which puts out a little bit of humidity.