The problem with that suggestion, as far as reality is concerned, is that HE shells (or heaven forbid, AP shells) would only do a miniscule amount of damage on a plane, and only on a DIRECT HIT!
I know what you'll be thinking now:
"Why a miniscule amount, its a huge shell filled with explosives!"
Right, but consider that all non-AA shells used a impact or time-delayed fuze, which would only activate if the shell impacts a sufficient amount of material...like the ships body, or its superstructure etc.
Its the same principle thats behind AP doing less damage to unarmored ships/ship parts. There is just not enough material in the way to generate sufficient impact force to activate the fuze - or at least, to get the shell to explode before it already passed through the plane...at best the plane would have a variably sized hole, which may or may not impede its ability to keep in the air.
AA Shells on the other hand damaged a large amount of the planes structure through bursting in the air and covering the adjacent area with shrapnel.