Boy, I never ever heard the word used in that context before, but guessed what it meant, (only because it is common to use a beard as a disguise). I knew, back in the day, that Rock Hudson's marriage to Phyllis Gates was to cover up the fact he was gay, as at the time, it was thought the knowledge might possibly damage his career, which was booming.
It does seem there a lot of folks who never heard the term, so am very surprised Days dredged it up, just so Jennifer could laughingly not consider them going to that play together as a "date".