So returning to the original question, will two nuclei having the same spin state decay at the same time? Is there any property of an atom that predicts decay time?
No, they have a fixed half-life, but the decay time is governed by probability.
Is there any property of an atom that predicts decay time?
Exact decay time, no. You're right on the $$$, there. There are properties that predict half-lives (probable decay times), but not actual decay times.