AFAIK they used a Theremin (Brian?) on
Please Go Home and the built in oscillator in the mixer desk for the effects on "Satanic". Moog's and other synthesizers were very rare to find in studios or to rent in the 60's.
According to the book
Analog Days Jagger bought a Moog modular system in 68 but it was never used on any tracks by the Stones. Brian and Bill were supposed to have been a bit pissed on Mick for never bringing it down to Olympic for them to play.
That Moog can be seen and heard in
Performance and also in the rare movie
Umano non Umano.