personally dont blame kunti for abandoning karna for the very reason you mentioned.It was wrong but a human action had i been in kunti's place i would have done the same perhaps.
i only blame her for never accepting karna as her son after rangbhoomi but only accepting it when it suited her.If accepting karna as a son would have affected her social status or soceity would have demeaned her then the same would have happened if karna would have accepted kunti's offer before the war .So what made kunti risk he social status before the war rather than after rangbhoomi?Only for the sake of her 5 sons.I just wish if she was ready to risk her social status for her 5 sons before the war she could have taken the same risk for karna's sake also after rangbhoomi
and to answer your question had kunti accepted karna as her son after rangbhoomi he would have been considered as a pandav.The same was pointed out by krishna ji in the epic when he goes to karna with his offer.Also as per shastras of that time any son born out of your wife's womb was considered to be husband's son that is why the 5 panadavs are considered pandu's sons despite having different biological father's.And being the jesht pandav would have changed karn's life in several ways.
Regarding kunti's guilt for karna or her revealing the truth of karna's sake.I dont agree with either.If any one can post any citation from the epic where kunti showed even slightest concern for karna after abandoning him would love to read it.Below is the citation when kunti decides to reveal to karna his truth i dont see a slightest concern or care for karna
Hearing these words uttered by Vidura, who always wished her sons the accomplishment of their objects, Kunti began to sigh heavily, afflicted with grief, and began to think within herself, 'Fie to wealth, for the sake of which this great slaughter of kinsmen is about to take place. Indeed, in this war, they that are friends will sustain defeat. What can be a greater grief than this that the Pandavas, the Chedis,the Panchalas, and the Yadavas, assembled together, will fight with the Bharatas? Verily, I behold demerit in war. (On the other hand) if we do not fight, poverty and humiliation would be ours. As regards the person that is poor, even death is beneficial (to him). (On the other band) the extermination of one's kinsmen is not victory. As I reflect on this, my heart swelleth with sorrow. The grandsire (Bhishma), the son of Santanu, the preceptor (Drona), who is the foremost of warriors, and Karna, having embraced Duryodhana's side, enhance my fears. The preceptor Drona, it seemeth to me, will never fight willingly against his pupils. As regards the Grandsire, why will he not show some affection for the Pandavas? There is only this sinful Karna then, of deluded understanding and ever following the deluded lead of the wicked Duryodhana, that hateth the Pandavas. Obstinately pursuing that which injureth the Pandavas, this Karna is, again, very powerful. It is this which burneth me at present. Proceeding to gratify him. I will today disclose the truth and seek to draw his heart towards the Pandavas
The way i understand this is that kunti didnt want this war because if panadavs dint fight poverty would be theirs and if they did fight still poverty would be theirs also she didn't want kinsmen to kill each other.She was sure Bhishma and Drona wont hurt panadavs because they care about panadvas but wasn't sure about karna and since he was very powerful she wanted to weaken his resolve to fight pandavas
atleast i cant sense any concern for karna here