No, blowing into a Nintendo cartridge will not help it work better. In fact, the moisture in a person’s breath can corrode and contaminate the pins on the game, making it more difficult to make a connection with the game system.
The belief that blowing into your Donkey Kong game cartridge when the game is frozen or not starting correctly to make it connect better is common. People think that they are cleaning it by clearing out dust, when in fact they may be damaging it even further. The original Nintendo system is known to have connection issues, most of which are mechanical. The system wore out at a faster pace than had been anticipated by the engineers. While sometimes a game may connect after having been blown on, it may be that the act of blowing on the game may have just given it one more opportunity for it to connect better. In the long run, blowing on a game will just add damage and distress quicker than normal.