Nope.
The total angular momentum of the earth moon system, which is spin angular momentum plus orbital angular momentum, is constant. (The Sun plays a small part as well, which will be ignored for this discussion.) Friction of the oceans caused by tides is causing the Earth to slow down a tiny bit each year. This is approximately two milliseconds per century, and amazingly this causes the moon to recede by about 4 centimeters per year. As the Earth slows down, the Moon must recede (this is an increase in orbital momentum) to keep the total angular momentum a constant. In other words as the spin angular momentum of the earth decreases, the lunar orbital angular momentum must increase. Here is an interesting side note: the velocity of the moon will slow down as the orbit increases.