Geometry generated from a modifier is not directly accessible until after the modifier is applied. Otherwise, we would be able to control each UV vertex of an object with a subsurf modifier before committing to it.
Please explain why you must keep the modifiers, so that we can help you find a change in workflow to answer your question.
For now, the answer is that it is not possible to apply UV mapping to geometry made from a modifier that hasn't been applied.
Here is an example of a possible work around that may meet the behavior of your 3ds Max reference. First, I'm making these assumptions about your workflow:
- You are using a repeating texture that doesn't rely on precise UV
- You are creating assets for rendering purposes.
- You are using Blender Render instead of Cycles (May work, I'm not
experienced with it.)
Instead of using a UV-map to determine the texture positioning , Assign a material and texture to the object and use its texture properties to map an image to generated coordinates using a cube projection.
The results will not be reflected in the view-port (You must use view-port shading set to material to see it), but creating a render will show the texture projected on all sides.