It will depend on the SSD controller, but AFAIK the DRAM usually isn't used for write caching. It's used to hold a copy of the bookkeeping structures which map virtual block locations to physical flash locations, which are mirrored on the non-volatile flash anyway, but are much quicker to random-read from DRAM.

If you use a DRAM-less drive in a situation where it can't DMA host memory, such as in a USB enclosure, it has to read those structures from flash on-the-fly which is obviously slower.