I would say that if the fan is used as part of a ventilation scheme, yes the dehumidification, and moving air displacing hot air coming from your skin is helpful. If you're in a closed room you just get the benefit of moving air, which tends to be marginal.
As for humidity, the evaporative cooling from sweat should aid cooling until you hit 100% humidity (at which point sweat can't evaporate). But we're just talking about the mechanics of cooling here. If we're talking about human thermal comfort, which has been (with some debate) empirically quantified, thermal comfort only exists within a narrow band of temperature and humidity. So for example, a person sitting indoors clothed with typical summer clothing, will only be comfortable at a temperature of 27C at a humidity of approx 55% or lower (see this tool for more info: http://comfort.cbe.berkeley.edu/)
As for humidity, the evaporative cooling from sweat should aid cooling until you hit 100% humidity (at which point sweat can't evaporate). But we're just talking about the mechanics of cooling here. If we're talking about human thermal comfort, which has been (with some debate) empirically quantified, thermal comfort only exists within a narrow band of temperature and humidity. So for example, a person sitting indoors clothed with typical summer clothing, will only be comfortable at a temperature of 27C at a humidity of approx 55% or lower (see this tool for more info: http://comfort.cbe.berkeley.edu/)