[yellowapple]

Eventually, yeah; just as the Moon is tidally locked to Earth, Earth would be tidally locked to the Moon.

I don't know offhand whether that would happen before the Moon drifts too far away to remain in Earth's orbit, however.

[sliken]

Moon is below escape velocity, so it's not leaving. In fact when 1 day = 1 lunar month the movement away will stop, and reverse. It will continue to get closer to earth until it hits the Roche limit and becomes a ring.