I absolutely love this poster, and upon close examination, I actually don’t think it would be that hard to achieve a similar look in Illustrator. What appears to have been done is a few simple steps repeated over and over again to create a more complex and appealing design. The background appears to be a simple lime green to turquoise gradient. The various swirls could be created using the pen tool or the swirl tool, and one simple swirl could be copied and pasted over and over and slightly edited to get the entire branch. Once the branch is created, it can be grouped and then copied and pasted over and over to create the many branches seen. The white branches could be sent to the back so that they grey ones are on top. For the border, they most likely drew one shape and transformed it then repeated the action, or created a border brush and applied that to the rectangle. The type tool could be used in the middle where an ellipse was drawn and then bordered with a fancy design, also probably using the brush tool. Although the design looks rather complex, it would actually be pretty simple!