Portland's owners have some of the deepest pockets in the league. Since giving Oden the QO will really cost them nothing but cash, I think it is a no brainer that they do it.
Particularly with the new GM in place, I don't think they want to risk one of their first decisions being letting a potential franchise center walk away, when all it would have taken to keep him another year was a qualifying offer.
The question of course is, will other teams make longterm offers large enough to entice Oden, forcing Portland to make a bigger decision. My guess is no. I think teams will be too afraid, and will want team options, etc. and Oden will just take the one year offer, and hope he can prove he deserves top of the market money.