The only question I have with Elmer's Carpenter pva glue is whether it will dry on doublers...I think on this application it will but can't speak from experience. Brett previously posted of doubles being wet after a crash with Ambroid (but isn't the same experience I've had) so I suppose pva could suffer the same. It's definitely strong enough and doesn't expand (like the Gorilla Glue I use which looks like expanding foam).
Being water-based, PVA and Aliphatic *will* dry, they wet the wood, the wood subsequently dries. It's not really a matter of strength in this case - even on hardwood, if you glue two pieces together, clamp them tightly, you can remove the clamps 15 minutes later and you cannot get them apart, you will have to use a chisel and cut the wood. Alphipatic, particularly, has tremendous "grab", even in a few seconds in tight joints - a fact that many model rocket people can attest to, if you are sliding an engine mount into a body tube and pause even briefly, or slow down, it will stick and be stuck forever.
It's different from Ambroid or other model cement - they are acetone or other solvent - based, not water-based, and will not wet the wood in the same way.
The best reason to use epoxy or cyanoactrylate (which is what I use), is to prevent it from warping from the contact with water.
Brett