Pretty much the title. From the start of the game I've been fascinated by the depth of the mechanics and characters. And of course I absolutely adore Jun.

Throughout the game I slowly discovering tips that the robo-girlfriend may be just an imagination of mentally ill main character. For example the soundtrack "She is real to me" and psychotherapist interactions. 

To be honest, mere thought that such a beautiful story could end up being just a "imaginary girlfriend" fills me with quite real pain and sadness. 

So, please spoil me. Would such thing be revealed on the day 40 or in some bad ending? Is it a mainline idea of the developers for all of those to be inconsequential and sad?

I don’t think so. Majority of people would be much more disappointed with this fact and gonna hate the game than if it is not the thing.

Would be real weird if she wasn't considering you take her on dates/introduce her to people. Unless it was an "All in Le head" situation for literally everything in game including people we meet (Would need to get Pyrocynical to make a 12 hour long video on this game at that point)

The "She is real to me" probably refers to how she is a robot, programmed to emulate and not a genuine human. Some would say it's just code, that none of her feelings and care are real, that it's all no more than imitation, simply fake. Like how during streams some compare her to a toaster. But to the protagonist she is more than just a lifeless machine. She is an important loyal companion and a lover who supports him even when he is at his lowest.
As for the psychotherapist interactions, I can't give any opinions about them because I never participated in them.