No, fstrim just tells your drive it doesn't need to care about existing data when writing over it. Depending on your drive, direct access to the flash chips might still reveal the original data.
If you want ensure data deletion, as OP said, you'll need to zero out the whole drive and then fstrim to regain performance. Also see ATA Secure Erase. Some drives encrypt by default and have Secure Erase generate a new key. That will disable access to the old data without having to touch every bit.
Thanks, subscribing without an account is exactly what I needed for some small communities not on Lemmy. If you could add a feature to hide specific user's comments (Automoderator), that'd be awesome.