Doesn't really match up with speechless. This english adjective is 99% of the times means that you can't speak because you're angry, excited, infuriated. aggrevated, shocked and blah, blah, blah. Безмолвный - nah, it's not used like this, it usually used to describe someone who doesn't like to speak much or when someone don't speak for some time for some reason.
On the contrary, язык проглотить, потерять дар речи and other similar expressions do match up with what speechless conveys.