Big IF...
if the original artist built the photoshop file with imported vector art as a "smart object" from Illustrator, you can double-click the Vector Smart Object file layer and it will open in Illy. Edit and save as new name at will.
otherwise, i have found exporting paths from PSD to AI not as exact as i prefer, ie:too many unwanted points. i find it's much cleaner, and just as edit-time consuming (do it right the 1st time) to re-draw in Illy.
for a 1st timer redrawing cut paths to fit psd files, here's a quick rundown.
-open new ai document, place image file (psd, tif, psd eps, etc), in layer1 palette double click for options and select to "dim images to 50%", lock layer (padlock icon).
-add new layer for vector elements, double click layer2 palette for options and deselect "preview" (this will give you a thin pen line for accurate redrawing).
-use pen tool to draw prefered cut path. i will quickly draw basic shape then go back and tweak for better fit. if you want to choke the cut so it cuts to bleed, create a negative offset path. for a white border use positive offest path.
-discard any unwanted objects, unlock layers, flatten artwork, save as a master file, save file with only desired cut path.
-i also will use one of the offsets to mask any unwanted extra "white space" if the original image file background is much larger than the desired image.
learn that the bezier pen tool is your best buddy. keyboard shortcuts while you digitize/redraw will make life much easier (and faster).
Good Luck!