It all depends on timing. I assume you mean for Buchanan to die after the election? Would it be accepted when a vice president, elevated to the presidential office by chance, makes such sweeping decisions while holding the office on a lame-duck basis? I honestly don't know, but it seems a bit iffy.
Alternatively, Buchanan can die earlier, before the 1860 election, making Breckinridge far more established as president, and also making him more of a shoe-in for the Democratic ticket.
I don't see that. Douglas men were a clear majority at the convention, and that's why the convention rejected a pro-slavery platform, leading to the Southern bolt.
They would oppose nominating Breckinridge to the end.
If Breckinridge is in office well before the convention, that might replace some of the Douglas delegates with more Doughfaces. But the Breckinridge forces need a 2/3 majority, so a small shift in delegates won't do it. It might be done with steamroller tactics.
That would influence the elections, but I still don't see Breckinridge winning.
If the Democrats nominate Breckinridge on a states-rights and pro-slavery platform, the Republicans win big. They will carry every free state as OTL, but by much bigger majorities.
Suppose Lincoln still wins, and Breckinridge evacuates the forts in the south just as you said. If he does that when he has just taken over for Buchanan a month ago, with the election already past, it would be very controversial. But if he has been in office for a year or so by that point, I can see it happening without too much fuss.
Regardless of how long he had been in office, it would be viewed as treason by Northerners. If he starts the drawdowns before the election, he could accomplish a lot though.