Unless you're an overseas visitor, the maximum package stay is 14 nights, which makes the maximum single
DDP stay 14 nights. If you're US based and are staying longer than that, for a package they must split it up into 2 stays.
So, yes, you CAN add a dining plan for your entire stay, but since it must be split into 2 stays, you will have to buy the minimum tickets for each stay (2 day for free dining, 1 day for paid).
I would assume, if AP ticketless packages are available at the campsites, then this would also fall under that possibility, which means that AP holders can book room and dining if staying at rack rate or AP discount rate, without buying separate tickets. There may be some accommodation for military discount stays as well (there used to be, I think).
As a note: All rooms on Disney property run by Disney are eligible for paid dining plans. The free dining promotion does tend to have resort or room level exclusions though (e.g. the villas and such sometimes aren't part of the FD deal).