Tinycore is here 12/1/2008! Welcome visitors.
That will save pulseaudio settings not pavucontrol settings.Some gtk3 apps save settings under /home/$USER and others use dconf.
No.I've never checked if you can backup/restore dconf settings, maybe you could make a test - I presume the settings are saved under /home/tc, but first you'd have to use dconf-editor to check if there are any pavucontrol settings in there.
There are no settings for pavucontrol in dconf-editor @Juanito.
So either pavucontrol saves settings under /home/tc or it doesn't save any settings and sets/mirrors what is set by pulseaudio.
alsactl store -f ~/asound.state
exittc
alsactl nrestore -f ~/asound.state