Yes water bowl placement will change the humidity in the air. Air movement over the bowl will also change it where the vents are also has an effect. BrianDallek yes warmer water evaporates faster than cool, and warmer air holds more water than cool air.

Sadly relative humidity is a poor measure as it varies. It is relative to temperature and it is expressed as a % of how what the maximum amount of water vapour the air can support. So as the ambient air temperature goes up it takes more water to reach the dew point (saturation) so 50% RH at one temperature is more or less than at another temperature. It is often said a heat lamp (or any other source that heats the air) removes moisture, when it actually it likely has little effect the drop in % represents an increase in the possible maximum.