The folks at Bard weren't aiming for scientific reproducibility; they just wanted to see what would happen. You can see more of the numbers broken down in the NYTimes article, but I want to mention the bit I found most relevant. Most of the 50 students who applied this way were public school students -- the article doesn't say how many exceptions there were total, or what happened to the private school students. Out of the 41 students whose applications were complete, 17 were admitted. All three of the homeschooled applicants got in.
I'm no statistician, but here's my bit of arithmetic. That leaves 38 applicants who were not homeschooled, of whom 14 were admitted. That's about a 37% admit rate for people who went to some sort of school, versus a 100% admit rate for people who didn't. In this very unscientific but intriguing sample, when the only criterion is the ability to do real college-level academic work, there's no apparent advantage to going to high school.
There are still a few colleges that won't consider homeschoolers. However, admissions offices at the colleges that will consider them -- now the majority of U.S. colleges -- generally say that homeschooled students end up getting admitted at a slightly higher rate than students who went to schools. It's pretty common knowledge, yet I've been in conversations in which people who opposed homeschooling responded by declaring, "But that's impossible!" Not that any of them could come up with reasons for admissions offices to lie about it, but their certainty was evidence enough. Whatever.
Homeschooling through a year of relocation has been hard. Homeschooling my extremely willful kid has been hard. There are things I worry about. But the one thing I don't worry about is whether homeschooling will have an adverse effect on my kid's eventual chances at college.