They wanted a 70's look and with CorelDraw, they got it!
I must admit, I don't draw everything I use in Draw by hand. Often, time simply doesn't allow for that. In this poster, the background was purchased from iStockPhoto.com.
I have created vine-like illustrations in the past using a drawing tablet and the freehand tool, then applying a Media Tool Stroke and tweaking the stems using smooth nodes and working with the curves until it looked right. Once a few are drawn, they can be duplicated and modified to create a variety. Hope that helps.