I had to think a bit on what your "yes and no" meant, as I would tend to agree with Luengo that the "click" sounds when typing in MSX basic (which is normal hardware behaviour) seem correctly emulated in MESS.
To understand I created a mess -wavwrite capturing the boot-up and me typing "ZILOG INSIDE". See capture below.
The graph visually confirms your point; MESS clearly generates an inconvenient dc-offset, which is indeed the cause for the plopping sound that can be heard when starting/stopping audio, i.e. on driver boot-up and when pausing/unpausing the emulation. Incidently I found that this plopping sound is magnified to a greater extent (not "plop" but a louder "poing") when "Enable X-Fi Crystalizer" is set to ON on my Creative X-FI soundcard.
From your explanation I understand that the issue is caused by the lack of the analog backend of the DAC in MESS, and in effect it's not an MSX specific issue as such. Which could also explain why Haze noticed similar behaviour with some games in MAME.
Not saying it should be resolved, but since the "SPEAKER" device apparently should be alleviating this problem: is there, give this MSX case, possible room for improving the dc-offset normalizing routine of that device, or would it need another solution?