Usually when people ask if a romantic relationship is going to "work out," WAMFBNIWTS, what they mean is, "Will these two cuties be together in a committed romantic relationship for the rest of their lives?"

True. Although some of us consider relationships to have been successful even if they end or drop the romance or sex, depending on what happened during or as a result of the relationship.

It's also generally understood that two people who are "together" in a relationship that "worked out" are public about their love and their relationship is embraced and supported by friends and family.
Perhaps generally, but not always. Many people throughout history have had private relationships denounced by some family that worked out.

Since your friend and their parent have no desire to make a public commitment and no desire to end the relationships they're in now — and going public would certainly end their other relationships, and not just their relationships with their (other) romantic partners — they'll never be "together" in the conventional sense.
Maybe they do desire to leave their current relationships or change their current relationships and make a public commitment, but because of prejudiced discrimination, they can't This relationship is literally still illegal in 48 US states and many counties.
I'm just saying... if they carry on with this affair for the next few years or decades... and if they make common affair errors like sending each other incriminating text messages... and if they're indiscreet and, say, ask their friends for input... and if they're okay with their friends sending letters to advice columnists packed with identifying details... well, the odds that it'll "work out" in the "get away with it" sense seem small.
Your friend needs to speak with someone who can help your friend see that they are not in love — not in romantic love — with their parent. GSA feels like romantic love, but it's a mis-expression, it's a mis-manifestation, of familial love, not romantic love.
This is where Savage gets it wrong. GSA can generate love. They might love each other. Most of his response is good, but that is a big miss.

Now, all of that being said, it IS a very risky situation for the friend and their genetic parent. Cheating should be avoided. If we don't want to be cheated on, we shouldn't cheat on others. But GSA is a tough thing to experience no matter what. Putting aside all moral concerns, the practical fact is that if one of the cheated-on partners finds out, then, in many places, they can use law enforcement to gain revenge, and otherwise ruin lives even where it isn't illegal.

In an ideal world, each of these people, if they wanted to be together, could have gone to their partners and either renegotiated their relationships or ended them, and then gotten together without facing criminalization and other forms of discrimination. But that's not where we are. We have to deal with the way things are even as we work to make things better.

These other entries here might help someone who is involved in, or around, one of these situations...
Should You Act on GSA?

If Your Partner is Experiencing Reunion GSA

GSA and Stepping Out