Yes, it does, assuming you want the information for a still image. There is probably a small amount of rounding error in there but it is extremely close. DJI publishes the field of view for all their drones on their website, you don't need to calculate it
The lens is about 4.5mm but in 35mm / full frame terms it is 24mm. The crop factor is approximately 5.3 so 4.5 X 5.3 = 24mm. Because the sensor is so tiny, a 4.5mm lens is needed to reach a 24mm equivalent.
The lens is 4.3mm, I think the EXIF is rounding you up to 4.5mm - I just used your numbers in the calculation for example sake.
The crop factor is a known entity because a 1/2.3" sensor is a known proportion of a full 35mm sensor. The crop factor is 5.62, but things can vary slightly because we don't know what rounding DJI has done. DJI says the Mavic Air has a 35mm equivalent focal length of 24mm, which means the actual focal length is 4.27mm, give or take with rounding. 4.27mm X 5.62 = 24mm.
The reason DJI can put such a small lens / camera unit on the Air is because it uses such a tiny image sensor. It's the same size sensor as are in a lot of high end smartphones like some variants of the Samsung Galaxy S phones, Google phones, or smaller point & shoot cameras.
A 1" sensor, like the one on the Phantom 4 Pro, has a crop factor of 2.7x for comparison. DJI says that drone has a 24mm equivalent focal length, so that lens has a focal length of 8.89mm give or take.