I know of this happening at least once. At Ça Va (bubbly bar where I am Wine Director), it’s basically a firing offense if anyone on staff tries it while working.
Yes. The normal pressure in a Champagne bottle is 5 - 6 atmospheres (70 - 90 psi). The corks are designed to resist that pressure, the loss of which makes removing them by hand near impossible unless the cork is old and dried.
Loss of pressure in Champagne over time would seem to be evidence that corks do allow some gas to leak, albeit very slowly, around the seal between the cork and glass.
Or…Have someone you don’t like try to open it using a corkscrew.
I brought a Champagne to a restaurant and paid the corkage fee. The server was brand new and started to pull out the corkscrew to open. I had to take over from there.