No. Without the Electoral College, one vote cast in a coastal city would be equal to one cast in rural Wyoming. Instead, because Wyoming has more Electoral ballots per person than larger states like California and Florida, a vote cast in Wyoming is "worth" about three times as much as one cast in those larger states.

A concern about removing the Electoral College is candidates won't spend time campaigning in more remote, less populous states. A) We have broadcast media and the Internet, you don't need to spend a lot of time in those states. B) Getting rid of the Electoral College doesn't mean getting rid of the state caucus and primary systems, there would still be plenty of in-state campaigning to win those (though typically not by an incumbent president).