Yes, it does. As long as your receiver is able to pick up sufficient satellite signals for a 3D lock (minimum of 4 depending on satellite positions).
It will give you elevation relative to the map datum you have selected on your receiver (the default datum is mean sea level according to WGS84). WGS84 is not adjusted for 'real' mean sea level, or for irregularities in the shape of the earth. A local datum may be, but is only valid in the prescribed region.
GPS elevation is, however, very noisy, with deviations of 100-200 feet over the course of a few hours being relatively common. This can be significantly improved by equipping the receiver with a high performance atomic clock. More commonly, GPS elevation is combined with barometric measurments, with the barometric sensor providing indication of short term movements, and the GPS measurements providing a baseline calibration for the barometer.