Don't combine the objects, export them both as a scene or individually too Mudbox and work on them separately....combining in Maya does no cutting of faces or merging vertices at all for modelling....I think you could be confusing this with boolean tools.

Try creating a sphere and a cube at the same location and combine them....then look at them in wireframe......In 3D terms you can consider this object, A Mess and pretty useless, On the other hand two objects combined that don't overlap each other is actually very helpful.

I am guessing you want to use a helix here to make a thread for your screw?

If so not a good idea as you will need to cut faces add edges and merge vertices and mess with the topology to no end to get a decent workable model for mudbox.
This method is fine and correct if you are using Solidworks but its not the way with Maya and polygons.

One quick and easy way to add a thread to your screw would be separate the head of your screw from the shaft, go to the animation menu and apply the a twist deformer to the shaft then reconnect it to the head, now extrude the faces you want along the length of the shaft to get a spiral effect of thread....you may need to set the twist deformer settings quite high on your start or end angle, obviously the higher the more turns.

If you are unsure how to separate and combine poly objects, heres how I would do it for your screw.

1, Select all the faces along the entire shaft up to the bottom of the head of the screw.
2, go to the mesh menu "extract" options, make sure that separate extracted faces is off and offset is 0 then click extract.

At this point you may be wondering what has it done as there is no visible change.

3, Go to the Mesh menu then select "separate".

You now two separate objects parented under the same transform node (view in the outliner)

You can select and work on both of these objects separately or select the parent transform and move them both together. or un-parent them. the choice is yours!

Apply the deformer to the shaft then make sure the shaft and head match up as close as possible using snap align and go to the mesh menu "combine"

Another alternative to struggling to match up the edges perfectly is simply combine both surfaces and use the bridge tool to add faces between the two open edges.

Don't forget "VERY" important always check that the vertices have merged together and you are working with a clean shell, the easiest way to do this is press 3 on the keyboard to smooth the model any vertices not merged will be very easy to spot. then get to work with your merge vertices tool.

Whenever you want to send models from Maya to Mudbox do your very best to make sure they are "clean" with nice edge flows and aim for modelling totally with quads
, some triangles are allowed but the bottom line is triangles do not subdivide well and can cause problems when animated after so hide them well if the object deforms.

Hope this helps you a little.