Yes, you'll get reviewed by the regular program if Bassett decides not to take your app further. I know of at least 1 person here who interviewed at Bassett but was offered an acceptance to the regular MD program.
Acceptances for the Bassett program may begin in December (they did last year, not sure if that's changing), but they're still made on a rolling basis. I personally didn't even submit the secondary until late October and still made it in (several of us interviewed in December and January, actually), so while time is a factor, it's not everything.
The invitation is still open to contact me with any questions about the Bassett program. We had a week of orientation in Cooperstown, which was completely awesome, then arrived in NYC with everyone else. There's no other distinctions between the programs in the pre-clinical years, although we'll likely be having some lecture lunches with some professors in the MPH and MBA programs (we had some absolutely fantastic lectures with them in our orientation week). Couldn't be happier with Columbia, it's a fantastic place.