At first glance I thought you were asking if it was possible to digitize the data, then I realized you were asking if you can get the pdf in....I dont think you can get a pdf in directly...What you should be able to do though is export your pdf as an image(.jpeg, etc). You should be able to then bring this image in and using the georeferencing tools get it to the appropriate location(cant remember the name and im not at the office, but basically identify 2 identical points on your data and something that is already georeferenced and it will scale shift and rotate to match). From there it should be basic digitization.
So I am able to import the image and now I would like to georeference it to the topographic basemap I have loaded, however, the georeferencing toolbar is greyed out. Am I able to take the imported image and put a couple points on it and reference it to the basemap and then digitize the polygons? And once I have each polygon digitized what is the process to relating them for each polygon will represent a different depth of a lake?
I've only ever done georeferencing once in the last 5 years so I'm not sure why that toolbar would be grayed out...but yes, you would identify control points on both your imported image and your basemap to tell arc that they are the same location.
As for polygons, once you have digitized them you would have to manually add the attributes as your imported image will not be storing anything beyond the color of the pixel.