Freezing ground turkey?
By "pillow-top package" do you mean the styrofoam package with plastic wrap that the meat came in? If so, I would wrap that package in heavy duty foil, and then put the whole thing in an air-tight freezer bag (such as ziplock). Squeeze as much of the air out of the freezer bag as you can before sealing it. The plastic wrap that meat comes in lets in too much air for long-term freezer storage.
I also don't know what that is, if it's the foam/plastic wrap packaging, then absolutely not, at least if you're planning on keeping frozen more than a week or maybe 2. Freezer burn is the big problem with home freezing foods and any air around the food will only exacerbate it. Remove, wipe off, wrap tightly in plastic wrap. If it'll be in there a while, put that in a heavy duty freezer bag. Regular plastic wrap is (surprisingly to most people including me), really not very airtight except in the short term. The heavier the plastic, the longer the food will keep in good condition. In addition to freezer burn, foods absorb and spread odors even in the freezer, albeit more slowly than in the fridge. The more tightly/heavily you wrap them, the less either will be a problem.