No. First of all we have to see where does this claim come from. You would have probably read this in a TOI article (Sorry unable to post the link).
If you revisit that article, it seems more like a inspired by thing rather than being a based on thing.
The director of Roy claims to be a fan of <PERSON> and <PERSON> and yes the two directors did have a two year affair, but let's try to examine what are the parallels between the movie's story and actual story.
1. <PERSON> has not been called or seen as a casanova, unlike the movie's character.
2. <PERSON> and <PERSON> are not two filmmakers based in different countries, unlike the movie's plotline.
3. <PERSON> and <PERSON> have not reunited after a split. 918
Well at least not until now :-)
So as you can see, apart from the fact that the story is about a love affair between two movie directors, there is nothing else.
But a mere linking of the story with some real life celebrities does spark an interest among the viewers, which is good for the business ;-)
So that's my take on this topic.
EDIT : While <PERSON> answer is factual, I would like to discuss a few things. The sources cited by <PERSON> are correct, but aren't they the same sources which intrigued the OP into asking this question ? Yes, the director claims that the story is based on real life characters, actors read extensively about the personalities and tries to get the nuances right. But this is what the claim is. OP wants to know whether this claim is right or not and we can answer this after analyzing the movie's story and trying to draw parallels between movie's characters, plot lines and the actual stuff. And as I stated earlier, there are none other than the fact the movie's characters are two directors. <PERSON> and <PERSON> are not the only two directors who dated each other. It would be interesting to know what similarities are there.
To me this claim is as good as Fargo's (TV series) - "Based on True story". 918