If you query Google Images with "full suspension backpacking", the results reveal several useful points:
* Yes, people can and do backpack on FS MTBs.
* Among the attachment points are handlebar rolls, seatpost-mounted panniers, seatpost/saddle bags and assortment of frame bags (inside triangle, over top tube, under bottom tube)
As an additional source of info, check out this thread on MTBR, it provides a useful anecdotes (for example about backpacking on FS MTB for 600 miles) and links (more relevant and useful resources).