As far as I know cellular contracts are not required on the tablets. And GPS works whether you have cell service or not.
The GPS will work (as long as the tablet has GPS...remember, Wi-Fi iPads do NOT have GPS), whether or not the tablet has cell service, but, if there's no cell service, and you haven't preloaded your map(s), while your tablet will know where you are, as well as where the drone is, you won't have any map to base actual location on.
As for the "contract" question, no, a contract isn't required...as long as you pay full price for the tablet. If you purchase from the carrier (or authorized carrier reseller, such as Best Buy, Costco, Fry's Electronic, etc), receiving the "discounted" price, then you'll be on-contract for whatever length they decide (typically, the usual 2yr agreement). If you plan to use the tablet for things other than just your P3, then it could be worth it to go with the contract, as you'll be saving $100 (or more) of the purchase price.
Alternately, you could do what I did. I've had a Nexus 7 LTE under Verizon contract since Feb '14, although I've been using it worth Wi-Fi almost exclusively for the past 5-6 months. Since its cellular-connected use has been virtually non-existent, and I wanted to get another tablet for exclusive P3 use, I found a new (Verizon) 16GB iPad
Mini 2 (ugh, I REALLY dislike Apple, but gave in due to the great iPad-P3 pairing) through Amazon (another company I've REALLY grown to dislike, being my former employer) for $300. Next, I called Verizon, and had then swap the SIM card numbers, thus activating the iPad
Mini 2 as "connected", and deactivating the N7 (effectively making it Wi-Fi only). I've even gone so far as to disable the N7's cellular radio, via 'Settings'. If you already have a cellular-connected tablet that you rarely/never use cellular connectivity for, and want a new-exclusive tablet for your P3, you could do the same thing that I did, thus you avoid adding another tablet (and contract) to your cell bill/account.