Tough call- we chose not to accelerate so I don't have personal experience in that regard.
First, second, and maybe third grade (as a long-time, in-class volunteer) seemed pretty easy. The "executive function" demands were minimal.
For fourth grade, it really ramps up, at least here. It's not enough to be smart; you have to fill out the worksheets on time, correctly, turn them in by the deadline, etc. Actually, I think those are important skills.
I would worry that if you skip someone from first to fourth grade:
1) They really might feel odd since physically, and emotionally, a first grader is very different from a fourth grader.
2) They might really struggle with the executive function issues.
Just my two cents.
