No, that is not so. Trump will continue the process he has been already heavily engaged in for several years, of destroying public trust in (i) the integrity of the voting process and (ii) the independence of the judicial system. You don't need to rewrite the Constitution to do that.
Trump has abundantly signalled his intention to exact retribution against those who have been critical of him. He has already said this will include political opponents, and has even suggested the former head of the US Armed Forces is guilty of treason. I consider it likely, given his previous form, that vendettas may extend to political commentators and media outlets unsympathetic to him. The Constitution gives little protection against that, as is shown by the experience of the McCarthy era in the US in the 1950s. The same, or similar, weapons can easily be deployed, Constitution notwithstanding.
My understanding is that the 2 term rule was only introduced into the Constitution in 1947 and that there have been several attempts already to repeal it. Trump has previously said he would like to see that set aside:
Donald Trump questioned presidential term limits on multiple occasions while in office, and in public remarks talked about serving beyond the limits of the 22nd Amendment. During an April 2019 White House event for the Wounded Warrior Project, he suggested he would remain president for 10 to 14 years.[31][32]
(From: Twenty-second Amendment to the United States Constitution - Wikipedia
My expectation would be that, provided ill health or death does not intervene, Trump may well decide to try to change the Constitution so he can stand for further terms, as Putin has done. Or he might try to bypass its provisions in some way. Declaring a state of emergency is a popular route in other countries, where a would be autocrat wants to stay in office, but there may be other ways.
Your Constitution gives a lot less protection against autocracy than some people seem to think.