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The choice of the value of U affects quite a few important properties including he Total Energy and the Fermi levels (thus the workfunction). However I want to know if the U term behaves just like an added potential term to the core for the atom.

Suppose I want to look at adsorption on a surface whose work function I want to vary in some range -X eV to +X eV. Then - is it allowed, with theoretical consistency, to do this by varying the U value over any range? Can it be said that in principle, varying U value is similar to just varying the potential of the surface/slab??

Adsorption involves the chemistry between the adsorbed atom/molecule and the slab. If the U term can affect the relevant bonds in the process, then adsorption energy will be changed. Just make sure that the U term corresponds to something physical, such as changes in the experimental conditions.