Thanks for your reply, and that is good advice about potential blockages when the drain turns from vertical to horizontal, especially below the concrete basement floor.
But all the diagrams of island venting I have seen show traps emptying into vertical drain lines above the kitchen floor then turning "horizontal" (with slope) below just below the floor, with the looped vent line running sloped slightly upward above the drain line. Some diagrams show a drain connection downward from the vent line to the drain to handle blockages.
What I am asking is whether the island drain line can run straight down to to a drain in the basement floor, rather than turning "horizontal" a foot or so below the floor. This would mean that the drain line would run vertically about 10 feet before it goes horizontal below the floor.