Is it possible to align a coil to a face?

[autodeskN884Q]

I have a conic shape which i want to (basically) emboss a coil on to. Is it possible to put that coil onto my surface? In this case i want the coil to just get narrower on the way up so it touches the face. It's meant to be a vase object with an embossed pattern. I hope its clear what I'm asking for.

[hamid.sh.]

How do you imagine it at the end? because with current profile it will look like this at top (I still haven't cut it from inside surface):

[davebYYPCU]

Yes, but not with a Coil.  Needs a few other tools.

Used a surface Sweep, cut for the Path of the Pipe.

You could combine / Join the two bodies before the Shell to remove the internal yellow faces, but not sure you want both bodies at this stage.

Might help.....

[jhackney1972]

Is this what you are looking for?  If so and you need an explanation, let me know.  If you want something different, please describe fully.  Model is attached.

Edit:  I attached another model with a full length spiral.

[hamid.sh.]

And if you want it completely outside, here it is (I added a fillet for smoother transition):

Edit: I should mention you can adjust Surface Offset to control how much your bodies overlap.

[autodeskN884Q]

This is exactly what I was looking for. Thank you.

Is there a better way than splitting bodies to only have the part of the coil that is on the outside? 

[davebYYPCU]

Did you read my post, 

if you Combine the coil body to the jug, before the Shell, no need to do anything else.

If you don’t want to Combine, then you could also Revolve Cut, the coil.

Might help....

[hamid.sh.]

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... Is there a better way than splitting bodies to only have the part of the coil that is on the outside? 

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Did you check @davebYYPCU 's post? He uses a simpler method for creating the path and had already addressed your question. As he suggested it's wiser to leave out Shell and after making coil on the surface use a Revolve to clear inside.