I am trying to draw a polyisocyanopeptide with different kinds of monomeric units that intramolecularly interact with one another. However, I wanted to show these connections with its carbon backbone in the helix configuration.
This illustration may be a combination of two images, or simply a program I don't know about. However, there are many (3D) protein visualisation programs that can show alpha-helices such as PyMol, VMD or Yasara. Here you can ray-trace the image (i.e. transparent background) and then combine the illustration with something else, e.g. an illustration from ChemDraw to produce something like the illustration shown in the question.
If you don't have a protein to visualise in these programs, you can simply download one (with alpha helices) from the PDB database.
Example of a helix visualised in PyMol:
This answer is for ChemDoodle, but I think you can import SVG files into ChemDraw as well.
Just take an SVG image of an alpha helix and copy and paste it into ChemDoodle. Or go to File -> Insert Image and select the SVG file from your computer. It doesn't have to be SVG, but they have advantages with scaling.
Made this using this File from Wikipedia, but if you have an SVG editor, you can make your own.