No. Say a particular model of SSD has over-provisioning of 10%, then even after writing the "whole" capacity of the drive, you can still be left with up to 10% of data recoverable from the Flash chips.
You should be running flash with self-encryption (and make sure you have a drive that implements that correctly).
To zap a drive you ask it to securely drop the self-encryption key. The data will still be there, but without the key it is indistinguishable from random noise.