Yes, electricity can flow through the air. But not in any way that really matters. It's more like a leak than a flow. There's always some ions floating around, and humidity makes it leak faster. Comb your hair and pick up small bits of paper with your comb, and see how long it takes the paper to fall. If electricity didn't leak through the air, the paper would stay stuck.
This is different from a spark. When the air sparks, the resistance goes down to basically zero and huge currents can flow. Without the spark, it will only leak. Slowly.