The star said the rehearsal room for Death Drop erupted into applause when they heard the show would be able to open on Friday.
The Australian performer, who was a runner-up in season six of the hit TV show, is appearing with fellow RuPaul veteran Monét X Change in the murder mystery comedy at the Garrick Theatre.
Courtney, who plays a 1990s pop star, said: “We took a chance and thankfully it paid off and the country is coming out of lockdown.
“I just prefaced everything with allegedly so I’d say we are allegedly opening on the 4th but there was a round of applause on Thursday when the announcement came over and the whole room erupted.”
The theatre has reduced capacity to comply with the Covid-19 guidelines and is also issuing contactless tickets, using track and trace and deep cleaning the building.
She said: “There won’t be a person in every seat but I think everyone is just looking forward to being back in a theatre and back in a live show with a live audience.
“I suppose some people might be familiar with something like drag race and with drag queens lip syncing to a Beyoncé song and this show is anything but that. It’s like a full West End Dragatha Christie murder mystery.”
Monet plays Summer Raines - a glamorous weather girl - in the show which sees a killer on the loose among guests gathered on a tropical island.
Courtney said: “If you thought 2020 was absurd wait until you see this.
“It’s just hysterical, it’s hard for us to keep straight faces in rehearsal because it’s so funny and so silly.
“I’ve found myself staring at my co-stars shoulder because I can’t look them in the eye or I’ll burst out laughing.”
Death Drop opens on Friday (Dec 4). Tickets are on sale from www.deathdropplay.com