Others have covered the practical parts a bit, so let's move on to the pharmacology of it.
In a cup of coffee you can get ~120mg or more of caffeine. That quantity isn't really large so filling the whole room with caffeine droplets / powder could be practical. The body absorbs most of caffeine, whether given orally or by inhalation so it should be fine either way.
- Rate of delivery
Here we may need to do some guessing. Let's say we want to deliver the 1 cup of coffee equivalent of caffeine (abbreviated cec as I made it up) over 30 minutes. Assume the room is sufficiently large and the air inside the room is well mixed, so the rate of delivery is mostly constant.
(inhalation is much faster than oral absorption, and we don't want to overdose our test subject, so a sufficiently slow delivery is necessary. Say the subject stayed in the room for 30 minutes after release of caffeine, the person will be dosed 1 cec instead of 6 if the delivery rate was 1 cec/5 min. Slower delivery rate gives better safety margin)
- Pulmonary delivery
On average human pushes 5 L/min of air through the lungs. Pulmonary delivery of drugs could be much more complicated tho. If the caffeine particles are too large, most of it would just hit the airways and be trapped within the mucus. This greatly reduce the rate of delivery (but much less so for the total quantity delivered, as the mucus will likely get swallowed as it is swept towards the throat).
In normal design of pulmonary delivery, we want the particle size to be within a small range, as too small particles don't have enough time to settle and get absorbed. While the data available are mostly not applicable as we tell patients to hold breath when using normal inhalers, you may still want to maintain the particle size somewhere within the optimal deposition range for pulmonary delivery (somewhere between 2 and 5 micron).
With some guessing / calculation, you may want to have ~0.8 mg caffeine (free base) /L in the room. Now we commonly use caffeine as a salt, e.g. citrate. Caffeine is only weakly basic but ideally you should use a mix of salt and free base to make a more or less neutral product, as you're going to breath that every single day. This is mostly not important but I just want to mention it. So let's skip the calculation and assume we have 1 mg/L of caffeine in the room.
- Indoor air quality (IAQ)
Let's assume all particle are 2 micron diameter, perfect sphere. That means they are around 4 μm3 in size. Caffeine density is 1.23g/cm3, so each particle weights about 5e-9 mg. To achieve 1 mg/L of caffeine in air, you want 200,000,000 particles in a liter of air.
Using Clean room as comparison is obviously not appropriate, but this value is much higher than FED STD 209E room air equivalent (or ISO 14644-1 class 9). From where I live in the IAQ standard is less than 180 ug/m3 of respirable particulates. Caffeine delivery obviously introduced a lot of particulates, potentially making the room hazy.
You better ensure that the particulate generator, caffeine / salt / solution etc. that you're using is sterile and free of any other contaminants. Afterall, the lung is not designed for absorption of solid matters, and some carefully designed drugs turns out to up cancer risk by just giving insulin through the lungs.
Your scientists were so preoccupied with whether or not they could,
they didn’t stop to think if they should.