Actually, as I think about it, it would only add the depth of the diagonal once - for the entire grid - regardless of how many rows there are. The outside grid position of every row would be exactly where they currently are; the inside grid position of every row would be 2/3 of our row gap behind where they currently are.

If we have say 9 feet between rows (I'm just guessing here), position 2 would start 3 feet behind position 1; position 3 would start 6 feet behind position 1, position 4 (1st on 2nd row) would be 9 feet behind position 1 (still offset), but only 3 feet behind position 3 and 6 feet behind position 2. With our staggered row positions you would still be 18 feet behind the bike (two rows ahead of you) that is directly in front of you.

Rather than clumps of three bikes, gap, three bikes, gap, etc, the distribution of bikes would be much more uniform. Rather than pole position being only a lane advantage, this would give a slight distance advantage as well.