Unwrapping those won’t be too hard. You’ll have to shop around through the Unwrap methods to find one that gives you a non-overlapping and fairly non-stretched result, but once you get to that point you can bake - it is not like you truly have to get the UV Map organized.
I know you probably don’t want to redo work, but I have a different approach for the whole thing I would like to throw out there in case the you end up needing a fallback plan. As it is, with the bake, you are going to have quite a bit of redundant data, and quite a bit of data, in the texture. You’ll have two tubes gradating from green to yellow in an almost identical way, but each will require its own pixels. What if you did this instead?
- Create a single image gradient that has the major colors in the corners and blends amongst them. Actually, I wouldn’t create this - I am sure you could get something from a Google Image Search - or even a screenshot from an existing color pickers.
- Make one tube, give it the classic tube seams (around the end circles plus one going lengthwise)
- Unwrap (probably using u,u then changing the tool option from Angle-Based to Conformal so that it comes out straight.) My thinking is that you’ll want the lengthwise quads to be rather skinny so the difference in colors around the circumference is minimal. In fact I would take the very left verts and bring them backwards to the same positions as the right ones (again, to prevent a color difference at the lengthwise seam)
- Adjust the location, rotation, and scale of this UV island. If your 3D Viewport is in Textured shading mode (Alt+z) you’ll see the result as you work.
- Now duplicate the tube, and reposition it a bit in both the x,y,z space and the u,v space. Each tube should occupy similar, but slightly different, positions.
Here it will probably help to put the UV/Image Editor into Island Select Mode so you can quickly adjust an entire tube with one selection click.
When you are done you will have all the complexity tucked away in the UV Map, and the gradients will be high-res even though the texture is not. I think my description may sound involved, but unless you run into problems somewhere I think you could recreate the entire spaghetti bowl in an hour or two.