Transparent Logo Puzzle
I have designed a logo that is meant to look hand-drawn, but I've converted it into a vector in Illustrator so that they can resize to their liking in the future.

Now she's decided that she wants some of the color to be transparent, so that paper color can be seen through the image once it's been printed, like this image below:
But I do not know how I might achieve this effect... If I printed straight from Photoshop, it would work. But what I usually do is import into illustrator then trace the image with the "high fidelity photo" preset so that it can be a vector file. And this creates solid white wherever there might be any transparency and "see-through" parts of the image. I could just keep working on this image in photoshop and skip making it a vector, but any printer that she would likely use would require a pdf to print from, which in my understanding loses all transparency as well.
Any ideas of how to get around this?
Thanks!!

