Just ... no. It can't.
First off it takes over 10ml of air injected directly into a large vein to cause any sort of embolism, 10 ml is a significant amount of air its quite a large syringe.
2nd, the veins are under your skin, in order for a BB to penetrate a vein it first has to penetrate through the skin and cause deep vascular damage.
3rd, the veins and arteries are under pressure, greater pressure than the pressure of the air, we know pressure flows from high to low, if any damage opened up a vein blood would be flowing out preventing air from flowing in.
4th Gas under pressure dissipates into the air, you would not be able to accurately flow 10ml into the small opening of a vein with a gun.
It is impossible to get an air embolus from a BB.