No, based on the provided information, Jerusalem is not situated directly in the desert.
Jerusalem's Unique Location
Jerusalem holds a distinctive geographical position that places it on the border of different climatic zones, rather than deep within an arid region. The reference states that Jerusalem is located:
"Lying on the watershed between the relatively rainy Hare Yehuda (Hills of Judaea) and the dry Judaean desert..."
This description indicates that the city is positioned on a transitional boundary – a watershed – separating an area that receives significant rainfall (the Hills of Judaea) from the arid conditions of the Judaean desert.
Being on this watershed means Jerusalem experiences influences from both environments. This transitional geography is also reflected in its diverse plant life, which includes both Mediterranean and Irano-Turanian vegetation types. Therefore, while the dry Judaean desert is nearby and influences one side of the watershed, Jerusalem itself is situated between this dry area and a more fertile, rainier region, not within the desert proper.