No, some SSDs use host memory buffer (HMB) to cache FTL tables. If the FTL cache gets corrupted, and that causes critical data to be overwritten, that could brick the SSD. For instance, if the FTL table was corrupted in such a way where a page for a random file is mapped to the page for the SSD's FTL (or other critical data), and the OS/user tries to write to that random file.
Yes, which is why they're cheap(er). It's better than the alternative of using flash instead of going out to system RAM, but DRAM-less SSDs are still the cheap option; HMB is a mitigation, and not a complete fix.