No, the built-in color property uses a built-in shader that does a multiply on the colors being rendered. Actually now you mention it the names are confusing - the 'Set color' action modifies the built-in 'color' property, which does a multiply, which is essentially the 'Tint' effect. However the 'Set color' shader effect replaces the RGB color channels when rendering.
No shaders actually affect the texture held in memory - they just apply processing when it's rendered. As a result you can use different effect parameters, and different built-in color properties, on individual instances.