You're off base on this one on several points.
1. Chainsaw carbs don't use air screws like most dirt bikes do. The small diaphram carbs use fuel screws which are basically adjustable jets, there is a low speed screw for idle and just off idle and a high speed screw for mid throttle to wide open throttle. You aren't adjusting an air bleed and chainsaws are not a high performance engine, even the most powerful ones are making far less hp per CC than a dirtbike.
2. The oil isn't replacing any air, it is changing the ratio of the fuel in the air. More oil equals less fuel, it's minor and even though the oil does combust with the gas it is in no way the same. There has been a lot of experimentation that shows that a heavier oil to fuel mix does need to have the carb adjusted to avoid a lean condition. Contrary to your thought process you can actually burn up a saw by running too much oil and not adjusting the carb. It's unlikely to make much difference going between 40:1 and 50:1 but if your saw is already slightly lean (most are from the factory) and you decide to run 32:1 or even 40:1 then your slightly lean condition becomes a definitely lean condition and the saw will run hot even though it's getting more oil. The oil plays no part in cooling the piston crown (does not readily vaporize like gasoline) which causes the crown to expand more which can lead to a few failure modes. One is a soft seize where the piston expands enough to hit the cylinder but doesn't melt and deposit aluminum. Two is where the crown gets hot enough to melt and blow out or smears aluminum on the cylinder walls. Three it gets hot enough to soften and begin to smear aluminum on the cylinder and binds the rings up.
3. The extra smoke you get with more oil is actually un-combusted oil, if it had combusted then there would be no smoke. This once again reinforces the fact that more oil leads to a leaner fuel/air ratio as a portion of the fuel/oil charge isn't contributing to combustion or evaporative cooling of the piston.