In general, does the presence of vegetation increase/decrease gross water loss (evapotranspiration) compared to barren land (evaporation only)?
I think it is best to introduce some definitions. Often in such studies, two types of evapotranspiration (or evaporation, but I will stick to evapotranspiration during this answer for convenience) are defined: actual and potential evapotranspiration:

Source: presentation called Water resources and their management in Pakistan by Jannat Iftikhar

As you have already stated correctly: when vegetation is present, the surface (generally) holds more water, hence more water is lost to the atmosphere. While barren land experiences more heating and stronger winds, the barren land tends to hold less water to evaporate. Consequently, even though the conditions allow faster and more severe evapotranspiration, there is just no water to evapotranspirate. 

The figure below shows an excellent example of this principle for two catchments in Saskatoon. Even though this figure isn't about an area facing desertification, it does exemplify the principle explained above.

Source: An Overview of Temporary Stream Hydrology in Canada (Buttle et al., 2012)

As you can see, the potential evapotranspiration is higher in summer for graph (a), whereas the actual evapotranspiration is higher in graph (b) due to its bigger stock of moisture.

To specify differences with respect to desertification, studies often compare catchments of similar size, meteorological conditions (radiation, precipitation, etc) but with different types of vegetation or different amounts/coverage of vegetation. 

For catchments where we have a water surplus, we can check the discharge of that specific catchment and the average precipitation (which produces the discharge when multiplied by the area of the catchment). The difference between the two is the water lost to other processes of which evapotranspiration is the main one.

For the barren land situation, different methods are applied. One could try to calculate the energy balance of the surface based on measured or estimated meteorological and atmospheric parameters. Another option would be to place an evaporation pan, which is basically a flat surface with a layer of water. Subsequently, one can determine how much water is lost from it over a given period of time (taking into account the precipitation).  

Sources: 

Iftikhar, J.(2017). Evapotranspiration. Water Resources &amp; their Management in Pakistan. 

M Buttle, James &amp; Boon, Sarah &amp; Peters, Daniel &amp; Spence, Christa &amp; van Meerveld, Ilja &amp; Whitfield, Paul. (2012). An Overview of Temporary Stream Hydrology in Canada. Canadian Water Resources Journal.