Answer:
The answer seems to be yes, the moon is gradually escaping from the earth's gravitational pull.
However, it is possible that this will reach a steady state, when the pull of the moon is less on the earth it will slow down or stop the rate at which the earth is slowing down its spin from the friction caused. This in turn will place a greater pull back on the moon and hence it may reach a steady distance from the earth.
However, it is possible that this will reach a steady state, when the pull of the moon is less on the earth it will slow down or stop the rate at which the earth is slowing down its spin from the friction caused. This in turn will place a greater pull back on the moon and hence it may reach a steady distance from the earth.