From your question I deduce ...

From your question I deduce that you are talking about annual water use of the tree rather than the moisture content of the tree itself. In comparison to grass vegetation, annual water use will be higher. This is because of the higher rainfall interception of trees (10-20% of P) in comparison to grass (<5%). Furthermore, non-irrigated grass will have seasonal water use due to its dormant stage, whereas the prosopis will transpire throughout the year, also because with its deep roots it has a much larger reservoir of water in the soil.

In general, you could estimate water use from potential evaporation (>2000 mm/y in Oman) using crop and moisture stress factors and taking into account rainfall interception loss. My estimate would be that annual water use of non-irrigated prosopis , or any other tree for that matter, planted to have closed canopy would exceed 1000 mm/y. That of groundwater irrigated date palm plantations exceeds 2000 mm/y. With substantially lower rainfall and groundwater recharge in Oman, this would not be sustainable. The annual actual use, however, also depends on the tree planting density and at low density (few trees per ha) water use would be reduced a lot and if the tree root system could enhance soil structure, infiltration and groundwater recharge it may become sustainable. I would be curious what alternative land use/cover would be considered, why you would be considering prosopis , and if there are native trees that could be an option.