Is this etymology for cheerio correct?

“Sedan chair” is the English name for a particular subtype of litter - covered, single occupant, sitting not lying down, usually just two chairmen.

…which reminds of the chairs at Castle Culzean (Ayrshire) which are designed so that servants at all-night parties can sit down for a bit, but are sloped downward, so that, if you fall asleep you are dumped on the floor.