Maybe but they will never admit it because to them it’s a weakness to reveal any kind of vulnerability.

Not all narcissists are the same for example my mum used to rage, smear campaign, did not care about the consequences of her actions because she wanted to win and not feel small. She never outright said this but it was clear through her actions. She pushed everyone away through her rages and tried getting people on her side by warping the truth through lies, smear campaigns and gaslighting. The only thing to do is not engage. Got her to see a psychiatrist, she’s taking meds and they’ve helped, she still believes she’s right but occasionally she says this mental health problem is eating away at her, “I don’t know what this problem is”. Never tell a narcissist they’re a narcissist because they’ll either call you a narcissist or they’ll look it up and find ways to manipulate you and other people. There’s another alternative which is family members taking the narcissist to therapy because they don’t stop their destructive behaviour, mind you in my case my dad was the one who wanted to take her because he didn’t want to divorce her (he’s a narc as well; the reason is he doesn’t want his reputation to crumble, divorce is taboo in South Asian culture and he’s doing it for his personal benefit not for his children’s desires).

Back to your question in my case I believe they do know they are different (eventually if people have told them that their behaviour is abnormal that’s when they start to have a little self awareness). BUT they will never stop lacking empathy, being less entitled, put their children before them, show humility or remorse (they will always try to prove people they were right and justified in their actions, say if the matter is about them abusing their children), they will still be grandiose etc. The only way they’ll stop is if they want to even if you take them to therapy they have to help themselves, no else can help them.

I’d say to not have the hope that they’ll change, you have to put yourself first, set and maintain boundaries always. Narcissistic parents can’t stand their children having boundaries, if they try guilt tripping you when you do that’s when you know that maintaining boundaries is working. People that used to benefit from you having no boundaries always do this. Over time they’ll stop but don’t expect them to be a healthy, neurotypical. If they don’t, go low contact or no contact if it’s possible and if you wish to, if not that’s still okay but continue to maintain boundaries.