I'm half-expecting to get shot down here, but I'll say no; not unless your eardrums are perforated or otherwise damaged.

In normal circumstances your eustachian tube links the middle ear to the back of your throat and exchange of air can take place. If the eardrum is intact then air should not pass to the outer ear. Presumably, if the eardrum is perforated, or has a grommet in it, then air can pass (indirectly) from the lungs to the outer ear. I doubt you'd be able to exercise though - you wouldn't get air in and out fast enough. It would probably be painful to try.

Pete is quite right. JBS Haldane accidentally, and permanently,  perforated one of his eardrums in his researches into decompression sickness.   It enabled him, as a party trick, to blow pipe smoke from one ear, and, though I don't know this for a fact, I am sure that he must have tried breathing through that ear as well.  As far as I can remember though, I never heard of its succeeding satisfactorily, and I reckon that it would be a very inadequate as well as painful channel to rely on.

Just a quick contribution from me:

If we go by a volume of 400-600 cubic centimetres per breath when breathing through the usual orifices, taking an esitmate of a large hole in the eardrum as 3.5 mm (the ear canal is around 7 mm wide), then we're looking at a flow rate of 9.6 cubic centimetres per second for a 4 second breath (which is roughly the time taken for an intake of breath through the usual routes). That's pretty high I'd say - but I don't know what the flow rate is for normal breaths. Does anyone else? And would that flow rate cause too much pressure on the surrounding tissue?

Of course there are lots of assumptions here, for instance the time taken to breathe in - but taking much longer would mean that an insufficient amount of oxygen would be delivered to the lungs.

All the best,

Kat

By the way you can hear through your Eustachian tubes.

You can try this when you have a loud source of noise at hand, like a jet engine or DJ speakers with lots of treble.

Put your fingers at your ears folding the flap, the Tragus over the opening to close them, then facing the sound source, open your mouth and yawn.

Some of the treble sound will be audible while the Eustachian tubes are open.

Quick and dirty opinions etc.

WRT sufficiency of volume of air: Try sustained breathing through only one nostril at rest and during exercise. Try this through a (shortened) straw or tubes of different diameters.

WRT smoke gets in my ears. I knew a real gentleman whose wife ran a kindergarden (creche) who could blow smoke out both ears, which fascinated the kiddies but horrified the parents.

I also have known a few people who could blow smoke out of their tear (drainage) ducts sometimes forming little bubbles before bursting forth.

WRT high frequency sound reception. I wonder if this response is not due to flesh pressure affecting the eardrum tension or the cochlear or bone conduction path. I have always "pictured" the Eustachian tube as being mostly a collapsed tube which requires a definite difference in pressure before any air is driven through (despite what the representaions/drawings show. (I am far from being an expert in this field but personally I have found - while diving or flying gliders - that I seldom "clear" my ears perfectly immediately and that normally perfect hearing only returns some minutes later, probably due to diffusion.