In the case you mention, grease residue on a dish; yes the surfactant would likely adsorb onto the grease via the hydrophobic tail. In fact, surfactants in detergents are known to absorb into a greasy soil before removing it. But the winner depends on the surface, the surfactant, and the solvent (in your example, dish water).
A good description of surfactant adsorption can be found in Milton Rosen's book or in the Book, "Surface Chemistry of surfactants and Polymers" by Kronberg, Holmberg, and Lindman
Check out the concept of "critical micelle concentration" or CMC. This is the amount of a surfactant required to form a micelle (an insoluble drop surrounded with surfactant molecules). If the surfactant concentration is too low, a micelle will not form and the grease will not be removed. If it is too high, you can form a double surfactant layer which will actually cause the droplet to redeposit on a surface.