Does this mean that deleted files will be rendered unrecoverable fairly quickly?
Yes, before you've even moved you hand away from the [OK] button.
Actually, though, it depends. If "delete" moves the files to a "trash" directory or "recycle bin" - there's no difference from a system without TRIM.
If "delete", however, actually "permanently deletes" the file - with TRIM it will be extremely unlikely that it is recoverable by any "find deleted files" utility.
Those utilities usually work on the assumption that the file system meta-data for the file is marked "deleted", but in fact the rest of the meta-data and the actual file data is still intact. These "deleted" entries will in fact be correct until the meta-data record or the actual file data is overwritten with a new file. If you run the "find deleted files" utility, it looks for meta-data records marked "deleted" - and will try to recover the file.
With TRIM, however, a command is sent to the solid state drive to notify it that the file data is free. The drive will add those sectors to a background task that erases free space and puts in on the available list. (Unlike a spinning hard drive, SSD sectors cannot be simply overwritten with new data - the sector (usually a "page" containing quite a few sectors) must be "erased", and then it can be written.)
The key to maintaining SSD performance is to ensure that the drive has a big pool of already erased pages. That lets a write completely quickly. If there are no free pages, then the drive has to move a bunch of sectors out of a page into partially used pages, and then erase the page, and then write the incoming sectors into newly erased page. This can make writes much slower.