So say you're recruiting an ineligible, and the player signs with you but doesn't come to school. Will he be considering you for next years recruiting? And if so, how much?

I don't have a DI team but, at DII, I've seen two scenarios:

1) He's considering you from the beginning of recruiting
2) He'll consider  you again after a little effort. Sometimes, just a phone call and schollie offer will be enough

How big of an advantage is it? Or does it all depend on how much you dropped on him when he didn't show up.

it is a percentage of the effort from the previous season.
My primary target one season was a very good player who was ineligible. I spent maybe $40,000 local on him hoping the extra cash would sway him into showing up. It didn't. He went juco 1500 miles away. But due to my effort $, the previous season, he showed up as considering me from the get go. I scouted the state, sent him a scholly offer and one CV. I then waited. At the 1pm cycle i showed as very solid on him and no-one fought me for him at all. He went from my most expensive bust to my cheapest stud ever.
Ineligibles are like a hard 4. They're a gamble, but when they hit they can really pay-off.