Was Mike the Gorfeins' son?

The movie is peppered with clues that point to the Gorfeins as Mike's parents:

• Timlin is a stage name. An internet search will show not one New York family with Timlin as a surname. Timlin is the Welsh diminutive of the names Tim and Tom, a reference to the Welsh poet Dylan Thomas. In the early 60s a name like Gorfein would not have helped a musical career
• Roland Turner, played by John Goodman, goes on a riff about how stupid it is to kill yourself by jumping off the George Washington rather than the Brooklyn bridge. The movie shows us three times that the Gorfeins lived on Riverside Drive - in the shadow of the Washington bridge. If Mikey grew up with them that would be the bridge that would loom large in his psyche, not the Brooklyn bridge.
• The conversation that starts with "I miss Mikey," segues to the Gorfeins. Musicians would have had hundreds of fans who had them to dinners and parties, yet Jean is so familiar with that couple that they need no introduction. In real life Jean might have joked "what the fuck is a Gorfein" or at least would have needed a moment to place them.
• In that same conversation Llewyn says he feels bad about losing the Gorfeins' cat and Jean responds "that's what you feel bad about?" There is nothing that we see in the story that could be worse than jeopardizing the family pet - the abortion would have nothing to do with the Gorfeins. Jean is furious at Llewyn and is implying that Llewyn is somehow complicit in Mike's suicide. Look at the despair in his eyes after she says that.
• Why would Llewyn take the cat in the first place? He shows no sensitivity to anyone else. He could have left it in the foyer and called Mitch. The suicide is the only plausible explanation - he can't bring himself to let them have yet another loss
• When Lillian apologizes for singing Mike's part, Llewyn responds that he is the one that should apologize. If Lillian is not the mother that apology would make less sense: singing Mike's part would have been an intrusion on Llewyn's grief and his response would have been rude but not so emotionally devastating.
• Why would Lillian know that part so well as to sing it impeccably if Llewyn was just a friend?
• much is made of the fact that the Gorfeins do not talk about Mike and introduce Llewyn as their Greenwich Village friend. But this is typical of what after a suicide: everyone tries to avoid making anyone else uncomfortable. So friends wait for the family to bring up the topic and families wait for the friends to talk. This movie shows that "conspiracy of silence"
• Jim leaves an important message for Llewyn with Mitch. This implies that the Gorfeins have a quasi-parental role with Llewyn. This is much more than a superficial fan to performer friendship.
• The apartment is almost certainly a Columbia University faculty apartment for families. It has several rooms down a long corridor. Persumably at least one room was an adult` childs' bedroom and judging from the size of the apartment there could have been several children. So why is Llewyn sleeping on an uncomfortable couch in a den? Often with the death of a child the room is kept as a shrine or is off-limits. Likewise, he may have chosen not to sleep in Mike's room for the painful memories it would evoke
• This one may be a stretch but I think that there is a hint that Mike and Llewyn were more than musical partners. The idea that Llewyns' affair with Diane, with whom we later learn he has a child, is part of the reason for the suicide. "That's what you feel bad about?" Also, that fits with the idea that Mitch is Llewyns' father figure and communication hub - Llewyn was the defacto son-in-law.
• Our first glimpse of Mitch Gorfein, before I put two and two together, was that this man was numb with grief. My impression of the Gorfeins is that they are bravely trying to live a normal life. I see the same awkwardness in all the five friends that visit the apartment. No one looked comfortable. This is exactly what happens after a suicide. The plot provides no other reason that would explain so much discomfort. This was the early 60s and these were academics and musicians in a far calmer, safer and more livable Manhattan yet the actors portrayed their characters as wooden.
• The Gorfeins are significant characters. The filmmakers provide no other reason to give them so much screen time. Nothing else explains the importance of these people in Llewyn's life.
• The filmmakers provide almost no back story. That is the perfect metaphor for Llewyn's inability to connect with people and for the conspiracy of silence that happens after suicide. It would be a different movie and a different main character if Llewyn were able to seek comfort for his grief. He can't or won't open up emotionally. I thought Stan Carps' performance as Llewyn's father was a brilliant counterpoint to Llewyn's emotionally illiterate personality. His face portrayed rich emotions.

By the way, and off the topic, all the reviewers missed the fact that the scenes where Llewyn wakes up in the morning at the beginning and end are the same footage except for one element - in the second iteration Llewyn does NOT let the cat out. So many people write about how dark this movie is but here is Llewyn back in the beginning, without a mark on his face, with a chance to go through the day again. Without the cat would he have to go to Jim and Jean's in the morning? Probably not. If he didn't know about the pregnancy he might have gotten royalties for his part in the hit record. To me this movie is highly redemptive. There is even an implication that he is remembering what happened the first time - why else would he stop to look at the poster of the Incredible Journey?

No, there is no definitive proof given that affirms that Mikey is a Gorfein.

There are plenty of moments in the movie where it would be easy to confirm that he is in fact their son, but such opportunities are never taken. For example:

• When Lillian says "I don't want to be in this room" she could have said "his room" which would imply more of a personal connection, but she didn't.

• When Carey says "I miss Mike," nobody else said anything like "Imagine how the Gorfeins must feel."

• If Mikey was the Gorfeins' kid, that would make Llewyn a total dick for the way he treated them (the whole abortion thing, etc.)

• Most grieving parents wouldn't have made Llewyn perform for dinner guests.

• There are no photographs of Mikey in the Gorfeins' house. In fact, the only reminder of him is the album If We Had Wings.

While this is all circumstantial and based on what characters could have said or done, it's more compelling evidence than we're given to believe that Mike is a Gorfein.