WI Sinatra follows Mia Farrow to India w/ the Beatles?

Here's a WI courtessy of Mrs. Khan:

In 1968 Mia Farrow, recently divorced from Frank Sinatra following a difficult 2 year marriage, went with the Beatles to India on their famous pilgrimage to Maharishi Mahesh Yogi.

Now, OTL Frank served her the divorce paperwork in front of everyone on the set of Rosemary's Baby. It seems the movie was running over and Frank was upset that she wouldn't drop out to be in his upcoming The Detectives, which she'd apparently agreed to do.

Now, let's handwave the whole mess. Suppose the studio doing The Detectives has a schedule problem and the filming is delayed half a year, so she's still on the hook to film it and he's satisfied for the moment. Now, this doesn't change the fact that the marriage was doomed, but let's assume it gives it another year.

So, after Rosemary's Baby ends, let's also assume that the divorce wasn't the impetus for her to go to India and that she wants to go ITTL as well.

Frank was known to like the Fab Four and covered a few of their songs OTL, so while I'm sure the whole Hindu "mumbo jumbo" is not to his liking, he might be persuaded to come along if only for the music and adventure.

So, after that long-winded set up...

WI Frank Sinatra is there at Rishikesh with the Beatles? How does this affect his music/career...or theirs? Could we see a Sinatra Indian album, or a Frank/Beatles team-up song?

How does this affect US Pop Culture with a direct bridge now there between the waining Rat Packers and ascendant Hippies?
 
India was a nice place for musicians to meet and swap techniques and to come up with song ideas. For example, John Lennon learned a guitar plucking technique from Donovan which would later be featured on the White Album. I don't know what Sinatra could learn, but the possibility is there.

Frankly, though, I don't know as if Sinatra would take all that much away from it; he doesn't seem like the peace and love kinda guy who wanted to learn nirvana from a foreign culture. So maybe he gets distracted from his career more than anything else.
 
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