The rope is actually at the top of the incline from the international gateway right at the main pathway around the lagoon. The United Kingdom will be to your left. Once the rope drops at park opening time, you do still have to walk through the United Kingdom and Canada to get to Future World. The folks at the International Gateway are definitely further away.
In all the times I've gone in through the IG, the only time I've had cast members push me along is when I've been in the park before official opening time. If it's after opening hours, they don't try to rush you through the UK and Canada, but absolutely nothing is open until 11:00 a.m., so other than to snap pictures without a lot of people in them, there's really no need to stop in these countries at that time in the morning.