Hi Ross,
It can definitely be done. As baumwolle suggested, you can import the photoshop image and use the autotrace tool in Illustrator. If the art is clean, it should trace fairly well with minimal clean-up.
If the art isn't very clean (lotsa fuzzy edges), the autotrace tool might not even be worth it. In this case, depending on the complexity of the art, it would just be easier to trace it by hand.
It might take a bit of practice, but this is how I would do it by hand:
Use the pen tool to create a closed shape by adding anchor points in key areas of the artwork. Then use the direct selection tool (white arrow) to manipulate each anchor point. It may require you to convert each anchor point by using the convert anchor point tool located within the pen tool to achieve the desired results.
Like I said though, it might take some practice, but definitely doable.
Unfortunately, there is no fool-proof, easy, quick way to convert rastor images to vector with a simple button click. Even the results from autotrace tool needs adjusting.