Most schools will get the application through without a problem, if they're interested in your kid.
And, most top prep coaches want a recruited kid for three years, not two. Yes, you'll see a lot of kids recruited for Junior year, but a lot of them then repeat, too.
But you are dead right about walk-ons not getting a sniff at the top recruiting schools. What coach is going to admit that a student there on his own merits is better than a kid the school is bankrolling to be there?
The more hockey-focused the school is, the earlier they recruit (e.g., Avon, Salisbury). The more academic-focused the school is, the later (e.g., Andover, Hotchkiss). The hockey schools actually develop talent further after they arrive and the kids can handle the coursework. The academic schools do very little development and are more worried that their hockey recruits won't be able to cut more than 2 years in their classrooms.