Yes, Poison has a chance to "fail to stack" when reapplied: when that occurs, it refreshes the duration instead.
Note that there is a (relatively late game, or at least late game in current content) passive ability that changes this behavior.
If you want to do a damage over time build before then, you might try working in Ignite and Melting. You can have Poison, Ignite, and Melting all going together without needing to pass any "fail to stack" checks.