No, it won't. Modern SSDs use data deduplication and compression to improve transfer speeds, to increase the amount of dynamic overprovisioning and to reduce write amplification. As a consequence, writing zeros to the SSD will only cause those zeros to be subjected to the hardware compression, that is an inherent part of the controller chip. What's more, data that only contains zeros has a very low entropy. It means that the effective compression ratio will be very high (and close to 100%). As a direct result from this, the number of cells (or pages, as cells can not be written individually in NAND) that will be written will be incredibly small, thus leaving all the sensitive data stored in NAND. That in fact is why the Secure Erase command exists anyway in the first place. Its entire purpose is to securely erase persistent old myths that continue to ride across various corners of the internet. lol