No, it can never escape. There isn't enough spin energy to achieve that. Given enough time, the Earth will slow and the Moon will move further away. Both the day and the month will get longer until they match at about 40 "days" (I forget the exact value, and that's in terms of today's "day", of course)

But, you also have solar tides which act to brake the Earth's spin so once the Moon is tide-locked to the earth, it will commence a slow death spiral as the Earth slows. "Furtunately" this will take many tens of billions of years and the Sun will explode* first.

* No it won't really explode - it will merely turn into a red giant and bake the earth to a crisp, then subside to a white dwarf and the Earth will freeze - or it would if it had any atmosphere or oceans left, but they will be safely boiled off so instead it will be cold and dry...

...forever**

**Well actually, not. but that's another story. Even the Universe must end sometime...