The TV show Friends did not invent nor inspire the term "gaydar" (and from your description, it sounds like they didn't even use it in the episode).

According to Green's Dictionary of Slang, the earliest found use of the term "gaydar" comes from page 42 of the February 11, 1982, edition of New York's Village Voice, in an article authored by Don Shewey:

"But the fear of gay men is not to be discounted. My gaydar tells me that up to 30 per cent of the men at the Santa Fe and New York weekends are gay, bisexual, or undeclared."

Another early instance of the term is found in the nationally syndicated advice column authored by Meg Whitcomb, during the week of July 24, 1986, as seen in Carlisle, Pennsylvania's The Sentinel newspaper:

Dear Meg: I have a question. How do homosexuals know who's gay and who isn't? When they meet a person for the first time is there some sort of special signal they have? I don't mean to put down gays in any way. I'm just Curious, Mo.

Dear Curious: I asked a gay friend your question, and here's what he said: 'There's no special signal, but a gay person can usually tell if a person he or she meets is homosexual. You've heard of radar? Well, we call it gaydar.'"

Green's dictionary also cites an article found on page 11 of the December 12, 1991, edition of the Bay Area Reporter, which defined the term explicitly:

"Gaydar: the mysterious ability of homosexual men and women to detect fellow homosexuals who may look, dress and act like heterosexuals."

The Bay Area Reporter had actually used the term as far back as July 1982 ("...no radar like gaydar, I always say"), but began using it with some regularity from 1991 and after. The term appeared more than once every year in that publication's pages at least until the mid-1990s.

The April 25, 1993, edition of the Washington Post also contained an article which used the term:

"You didn't need Gaydar -- that mythical tracking system for spotting other gays -- this weekend in Washington. Everyone was gay, it seemed."

By the end of that same year, the LGBTQ lifestyle magazine Out had published the word.

In the November 12, 1993, edition of Lehigh University's student newspaper The Brown and White, the word was used in an article about dating on campus:

"James Truver, '95, a journalism major, announced his homosexuality publicly during his freshman year at Lehigh. According to Truver, men do meet other men at fraternity parties on the Hill and hook-ups do occur. The only difference is that it is more secretive.

"'We have this little joke called gaydar, gay radar,' Truver said. 'A guy can walk into a room and he'll know right away if someone is gay, it is a feeling. You will see who they are talking to, and follow them around with your eyes. Everyone gets drunk and then a guy will bring another guy into their room. They have to leave quickly so no one finds out. It is secretive, stressful and shameful. It just doesn't work.'

"Truver met someone last year at Lehigh. The student had not publicly admitted his homosexuality. Such people are commonly referred to as 'closet gays.'"

So, there's at least evidence that the term was in use among the LGBTQ community in New York, California, Washington D.C., and Pennsylvania by the end of 1993. And it had been featured in at least one syndicated column with some national distribution in the United States. "Gaydar" was likely fairly widespread by the early 1990s.

In addition, the Usenet Archives database returns hundreds of different posts from the pre-world wide web days of the internet featuring the word "gaydar" that were written between October 1991 and June 1994, though it does seem to be confined to two or three specific threads that gained hundreds of replies.

The TV show Friends did not premiere until September 1994. By then, it would appear that the term was already established.