Whenever we go to Epcot we always walk through the WS to get to Future World when we are staying at the Epcot Resorts (BC/YC/BW). You shouldn't have a problem walking through there or taking the boat to Epcot as well.
The boat from Beach Club will take you to outside the International Gateway entrance. They don't go into the park, those are separate boats on World Showcase lagoon.
The International Gateway entrance will open either at park opening time (9:00) or a few minutes before to allow you to walk up to Future World. There is a "rope drop" near Innoventions by the Pin Stand at 9:00 to allow people to actually go to the attractions.
The boat and the walk take you to the same place: the International Gateway entrance to Epcot. The boat does not actually take you into the park. You can enter Epcot through the IG prior to 11 am when World Showcase is open and then walk through WS to get to Future World. How you get to IG is up to you.
We have stayed at the BC 3 times in the last 2 years and there was never a time we would even consider taking the boat over to the International Gateway. It's such a nice, relaxing and short walk that it made no sense for us to talk almost as far to the end of the boat dock and then most likely stand and wait for a boat to pull up and take us over. We would already be through the gates and into the park if we took a short stroll.
I would walk too, even if the boat is there when you get to the boat dock, it takes longer to get to IG then walking, because it stops at the Boardwalk first.
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