Nope, because they will both end up at the same temperature, namely, the average temperature halfway between the two previous temperatures.

In a countercurrent heat exchanger, the hot air will get colder and colder until it is at the same temperature as the cold air, and the cold air will get hotter and hotter until it is the same temperature as the hot air.

This is because the hot air is not warming up the same air molecules that it relies on to cool down, and the cold air is not cooling down the same air molecules that it relies on to warm up. Each current of air gives up a part of their heat/coldness, becomes colder/hotter, and then moves towards a section of pipe that's even colder/hotter than the previous section of pipe.

A picture is worth a thousand words, although it takes some staring and studying before the concept finally clicks: https://en.wikipedia.org/wiki/Countercurrent_exchange#/media...

Ah ye thank you makes sense.

There is a diagram illustrating why not in the wikipedia article: https://en.wikipedia.org/wiki/Countercurrent_exchange