It depends on the firmware running on the SSD, so theoretically it’s possible but practically it’s not. Instead, SSDs use a special command to zero all cells on the chip at once, so it’s all or nothing. You can’t target specific files.
The filesystem may choose to store new data at different logical block addresses than older versions. The SSD will definitely choose to store those newly written blocks at different physical addresses, both for the sake of wear leveling and for performance, because a read-erase-rearite cycle on an entire NAND flash erase block (several MB at minimum) is a very slow operation.
