On the contrary, your olfactory epithelium - the bit that does the smelling up at the top of your nasal cavity - doesn't absorb smells. The olfactory receptors bind small molecules reversibly.
However, the olfactory epithelium has a coating of mucus, and so small molecules dissolve in the mucus in order to meet the receptors. Molecules will also evaporate off this mucus, but some vanishingly small fraction of the odorant in a room may stay in the mucus of the nose and the upper respiratory tract long enough to be moved by cilia to the stomach.
I think that for water-soluble molecules, the surface area of mucus lining the airways that odorant can reach is a more relevant factor than the number of a particular receptor (which is very low); but depleting a room of an odorant (which is concentrated enough for you to sense in the first place) by breathing would surely take an extremely long time; as the concentration dropped the remaining molecules would become 'harder to catch', and you'd suffocate first in this enclosed space.
Interestingly, hydrophobic molecules that do not readily dissolve in mucus may be bound by soluble 'shuttle'-like proteins which bridge the gap to the receptors: http://www.ncbi.nlm.nih.gov/pubmed/12044155
These odorant-binding-proteins probably contribute to the diversity of molecules we can smell, and presumably also bind odorants reversibly and may release them back in to the nasal cavity.