@Rinoa sorry for the late reply, little one is keeping me busy!
In my case because I was 41+6, they let me go home after the pessary was inserted. Contractions started at home a few hours later, and I went back in for monitoring as they were very close, at which point my waters also broke and I stayed in from then on - with my partner allowed to join.
Had I been 42+, my hospital policy would have dictated that I stay in after pessary as that's considered higher risk.