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I'm trying to model an object where the 2D tube shape it rolled up along the sides, similarly to how you roll your sleeves up

Rough Sketch of cross-section

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You could start with a plane and delete one side.

Add plane delete edges

Then add a Subsurf modifier to make the curl smooth. Add a Cast modifier driven by an empty. Then a screw modifier to wrap the distorted edge around into a tube.

Curled edge

Tube

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Create a Bezier curve. Open edit mode, rotate it by 90 degrees in Y and 90 degrees in Z by, offset it in X direction, add a screw modifier and edit it from front view. You can add a solidify modifier afterwards.

The cool thing about bezier curves is that they are a bit more flexible than regular polygons.

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