I wouldn't be certain of that, especially in the case of Bell supporters. They were mainly ex-Whigs who wanted to paper over the slavery issue. Some will stay home rather than vote for a Democrat and others, especially in the north, would vote a fellow ex-Whig than a Democrat. You'll also have a fair number of Breckenridge supporters who stay home as they don't see any difference between the two and would rather just go ahead and get secession in place.
I think it would be a close race, close enough that I could see some states decide to secede before the runoff took place rather than take their chances, in which case, Lincoln wins, otherwise, Douglas probably wins in a squeaker.