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The title does, prima facie, appear absurd.
Performing a swallowing action whilst pinching the nostrils shut gives the impression of listening through a bucket filled with water around the head; audible sound levels are perceptibly reduced. Some humans may encounter a similar sensation blowing their nose - hard.
This makes sense give the ears connect to the mouth/nose through the eustachian tubes. Can an odour make its way to the olfactory sensors through the ears?
A quick diagram to point out to people who may not know what Eustachian tubes are (#2).
In order for the aromatic molecule to reach the olfactory bulb, it would first have to get through the Tympanic Membrane (#22) [a.k.a. - Eardrum]. The Tympanic Membrane is water/airtight unless pierced.
So, while it's plausible that an aromatic molecule could travel through the Eustachian tubes and enter the pharynx areas, there isn't any way to get into the middle-ear in the first place unless the Tympanic Membrane has been compromised.
In a healthy and intact individual, the answer should be No.
@MCM gave a succinct and accurate description of how a healthy and "normal" person will not be able to smell via olfactory sensing trough the Eustachian tube.
Here is an interesting concept in which the brain is able to confuse senses, or alternatively, use sensory input as a metaphor for interpretation via another sensory output. This is a condition known as synesthesia. The majority of known synesthetes have cross-talk between audio-visual sensory pathways. That is, one may interpret sounds as shapes or colours, while another may interpret specific objects (or symbols) as colours or sounds. There were a handful of synesthetes studied in the late 1980's (referred to in this article by Day S.) and one patient was able to interpret sounds as smells. In the review article, smell-interpretation of sound accounts for ~0.1% of known synesthetes, while sound-interpreting olfaction is more common at ~0.6% incidence. On some higher level, the neural information for two senses is confused, and synesthetes that may confuse smelling for some other sense, can not technically perceive scent (using olfactory receptors) through other sensory organs (like the eyes), so the answer is technically no.
Modified 6 Dec 2012: One approach to this question is to perform a sequence similarity search for genes encoding genes with a functioning in sensing external stimuli, be they olfactory receptor, taste receptor or other such genes that are expressed in cDNAs or RNA-Seq data from library preparations of the appropriate ear tissue. While there is not likely at this point in time to be much data available in RNA-Seq format, one might find cDNA libraries from cochlea or neighboring tissue.
A "hit," meaning there is evidence that, for example, an olfactory receptor gene is expressed in cochlea, eg, only means that there is potential to smell through the ears. Taste receptors are expressed throughout the alimentary canal in humans, but tasting the contents - food or other - is not readily perceived as de facto taste outside the oral cavity. Nonetheless, there is no reason not to expect such sensors are expressed to relay information to the brain as to what is or is not present. "Smelling" in/by the ear for the purpose of detecting the presence of a given entity or molecule could serve a similar function.
