Not exactly. There is some loss, as you so astutely observed. The reason (for those less astute) is that at higher latitudes, the eastward rotation of the earth is slower, and at maximum at the equator. A rocket launched from the equator has about 1,000 mph "free" speed boost. The farther north you launch (assuming eastward orbit) the more of that lost initial velocity you have to overcome.
Math is not my forté but I'd guess that a launch from 45 degrees north latitude would sacrifice about half the equatorial boost.
