If I recall correctly, I'm not sure you can do that to securely erase it. The controller electronics that take instruction from the OS internally implement routines for properly wearing the SSD cells evenly; they have a finite write/read cycle, and if you keep writing them over and over they "die", and so the internal system distributes write instructions to prevent issues with the drive. Your best bet would be to write data to completely then erase the file(s) and do it over again. You'd then shorten its life in the process, and even then there may be space that isn't overwritten in the process as I believe there may be some excess space saved for other data and/or backup space for found bad cells.
If you have security requirements for eliminating data on old storage media, you may not want to use SSD's or you might want to look into something more old fashioned, like shotguns or metal shredders.
If you want to restore performance, you need the drive to support TRIM; most manufacturers are coming out with utilities for their own drives that will refresh the drive. As time goes on operating systems are coming with TRIM support built in.
In a few years you probably won't have to do anything to maintain the drives. It's much like defragmenting a drive. OS X already defragments files that are less than 20 meg. Most Linux filesystems are pretty good at keeping fragmentation down. It seems NTFS still has issues with it, but I think at some point it'll be reduced as the file-within-a-file concept gets more popular in Windows (think ISO images and VM drives).
So to answer the question...zeroing out the drive will not restore performance the way TRIM support and manufacturer utilities will.