Legion is supposed to be a glimpse of David's mind and thus the unreliable narrative of the episode works since we as a viewer do not know which is real and which isn't...
Coming to the sequence, the song itself was supposed to showcase the love blooming between David and Syd and the director felt like a Bollywood style song is worth it since Bollywood relishes in musicals when it comes to love songs...
“The show is based around the idea that we’re going to give you this objective feeling of what it’s like to be David, and what else does falling in love feel like other than a Bollywood dance routine, really?,” says Hawley, who both wrote and directed the episode. “It started out as something small and then it turned into an entire day of production.”
“We choreographed the whole thing to a real Bollywood song and I ended up using a Serge Gainsbourg song, which added to the surreal-ness of it,” Hawley says, adding that the final music “has a Bollywood feel, but is not what you would expect.”
This reinforces the unreliable-narrative concept of Legion and thus adds to the weirdness...
Source: http://variety.com/2017/tv/awards/dan-stevens-threw-up-noah-hawley-legion-bollywood-scene-1202454941/