It may allowable. Someone with standing would have to sue afterwards and we’d see what the Supreme Court says.
You live in dreamland though if think that Canute Harris would ever resign, if she had children she would sacrifice them to Baal to be in the big chair. Biden won’t resign either unless he starts publicly crapping himself (more often than the one time we know has happened in the Vatican).
The 22nd Amendment states that no one may be elected president more than twice, and no one who has served over two years of a presidential term to which someone else was elected may be elected more than once. So Barack Obama may not be elected president again.
But ... a plain reading of the 22nd Amendment would certainly permit Barack Obama to be elected or appointed vice president, and then accede to the presidency, since he would not be *elected president* for a third time. There is no limitation in the 22nd Amendment regarding *serving* as president even if one has been elected president twice; had the amendment prohibited persons twice elected president from serving as president, it would mean that Reagan, Clinton, etc. would have had to resign the day after their reelection.
The question then would be whether the 12th Amendment, which clarifies that “no person ineligible to the office of President shall be eligible to that of Vice President.” The key words are “ineligible to the office,” and, unless Barack Obama actually was born outside of the United States, he certainly is eligible to the office (i.e., to serve) as president.
So, yes, Barack Obama is constitutionally eligible to the office of vice president, and could be elected or appointed (the latter pursuant to the 25th Amendment, which would require confirmation by both houses of Congress) to the vice presidency; he also remains eligible to the office of the president, although he could not be elected president and would need to accede to the presidency pursuant to the line of succession.
But I agree with Impy that there is no way that Kamala Harris would resign the VP now that being appointed to the Supreme Court (the only thing that might tempt Kamala) is out of the question due to KBJ’s certain confirmation. I’m not so sure about whether Biden would resist the call to resign if Obama, Clyburn, Schumer, Pelosi, Klein, etc. all said that it would be a great patriotic act for him to resign in favor of his VP; only because Biden stumbled into the worst VP imaginable, someone who would sink Democrats’ 2022 hopes even more where she to become president, is a Biden resignation unthinkable for Democrat bigwigs.