No, Donald Trump's vow to leave his business so he can focus on running the country will not quell concerns over his conflicts of interest. Trump vows to leave his business dealings up to his children. This is the opposite of an ethical decision. It is hard to believe that with his children at the help, Trump will remain completely removed from the dealings of this business.
Though I wish this move would quell that concern, I highly doubt people will be happy with it. The company will still feature Trump's name so it will still be another promotion for Trump. If the company fails, people will question Trump's decision, and if a scandal happens to come to light, Trump will be blamed. For this cause, Trump would still be worried about the success of his former business.
No, concerns regarding Trump's conflicts of interest will not be quieted if he leaves his businesses during his presidency. The only acceptable course of action will be for president elect Trump to put his businesses into a blind trust before he takes office. Transferring the day-to-day operations to his adult children will merely shift control temporarily and still be subject to undue influence.
Mr. Trump's detractors will not be satisfied regardless of his actions. There is a segment of the media and the populace in general that simply believes that Trump is evil incarnate. That segment of the populace and media will always question whether Mr. Trump is acting in his own personal interest