So there's a player who I recruited when he was a freshman. He was considering my school and another school for quite a while. Ultimately, I withdrew my scholarship offer (yes, I am an idiot) and the other school he was considering filled its final slot with another recruit.

The player went to community college for a season.

Going into next season, will I have any advantage over an otherwise identical school that this player did not consider when he was a freshman? If so, is there any way to quantify (in $) what that initial advantage might be?

To my knowledge, WIS has never stated what your advantage is, but coaches have speculated it's about 25% of your previous efforts.  It's possible, but rare, that he'll be considering you from the beginning

Keep an eye on him. 
I initially signed a guy but he went Juco about 1400 miles away.  The next recruiting season he wasn't considering me from the beginning but I did sign him with only the $100 for a scholarship.

ages ago, support told me that 25% would be a good estimate of the carryover

Do you think the fact that I withdrew the scholarship offer at the end impacts any possible carryover?

No, I did the same thing in Naismith, except the guy signed with the other team, but was ineligible and went juco.  The next year he was again considering the other school and mine, even though I put no further effort into him and that he actually signed with the other team the previous season, he still considered my school until signings of the next season.

I am pretty sure it is 25% of the effort, not of the money, just recruited an 800 something rated guy twice, first time 50 miles away, spent 50K, second time 1800 miles away, spent 50k plus, my first offer the second time was $100, a start, and 20 minutes, which got me considering myself and others but ahead of the other school, so I would guess 12.5k of local effort carried over (which is nothing to sneeze at from an A/A+ prestige school)

it has to be 25% of the effort