I'm quite sure they will fit under the seat (you can lay them down and put your feet on them worst case). Also, for basic economy they enforce the no carry on at the gate (ie you will be group 7 or 8 or whatever and the gate agent will make sure you are not taking any carry ons), so once you are on (and worst case they dont fit) you should be able to stick them in a bin? As far as I can tell once you are on board the FAs can't tell if you are basic economy.