Possibly, but not by living on nice smells
Let us assume that the Astomi have energy requirements comparable to humans. Looking at the Food energy article in Wikipedia:
According to the Food and Agriculture Organization of the United
Nations, the average minimum energy requirement per person per day is
about 7,500 kJ
Looking at the energy-dense foods in my pantry, Nutella's nutrition information label says that it has 2228kJ per 100g. So, if sufficient atomised Nutella is being sprayed into the atmosphere where the Astomi live, they are viable if they can absorb about 330g each day. Unfortunately, naturally occurring sprays of atomised Nutella are not a feature of even the most friendly fantasy world, so an alternative food source will be required, but this gives an idea of the minimum mass required.
Note that a large proportion of human energy is expended on running the brain and/or regulating the body's temperature - by making the Astomi cold-blooded and or small-brained they will require significantly less energy. On the other hand, if you want them to have greater-than-human capabilities then they will require a larger energy budget.
Can they live on smells?
At this point a quick thought experiment is in order. Imagine that there is a 4m x 4m enclosed room divided up into a grid of 1m x 1m squares, with one Astomi sitting in each square, for a total of 16 Astomi. (Assume a ceiling height of 2-3m.) Now imagine that 1g of strong perfume is sprayed into the air in this room every 15 minutes for 24 hours - this is a lot of perfume, resulting in a room that would be absolutely reeking by the end of the experiment. However, this is still only 96g of perfume between 16 Astomi - even if the Astomi absorb every single molecule of the perfume they have only received 6g of nutrition each. The perfume would need to have an energy density more than 50 times that of Nutella in order to provide adequate nutrition. So odours (pleasant or otherwise) are not going to cut it, the Astomi definitely need something more substantial.
Possible sources of nutrition
Given the requirement for feeding to be invisible to the naked eye, a few options, possibly used in combination, are:
- pollen: The Astomi brush past flowering plants and catch the pollen on their hairs, subsequently absorbing it. They will need to brush past a lot of flowers in order to survive this way given the low pollen mass per flower, which will mean they have a higher energy budget and will need to be nomadic in order to give the flowers in an area time to recover before they feed again.
- insects: Possibly Pliny the Elder had it backwards and the Astomi actually emit smells that attract insects. The hairs then trap the insects and draw them into tiny pockets hidden beneath their hair akin to the pitfall traps of pitcher plants, where they are digested and the nutrients absorbed. A variant of this would make the Astomi anteaters - they sit or kneel down on an ant nest and appear to a surface observer to be sniffing the air, while below the surface the specialised long hairs on their buttocks or knees are diving into the ant nest to seize ants and larvae then drawing them into their digestive pockets.
- Honey: The nutrition label on the tub of honey I am looking at says it has 1401kJ per 100g. So if the Astomi have hairs that can slip into a beehive and escape unscathed they can definitely do pretty well from a hive. However, this encounters the same issue as collecting the pollen themselves - they need to have a large range before the resource will regenerate.
In short, the Astomi are plausible insectivores, but not odourvores.