I've seen it happen in Europe but specially in Spain once and again since 2011. It's not his actual intentions what you must be wary about, or whether he has sincere Dem allegiance or not. What you must worry is the fact that even as a classic defender of Democratic Socialism he simply won't be able to do much, not in this day and age, an that has consequences.
As an example of one of his viral videos, he says legal systems for expropriating exist in NY, but that doesn't matter much because he will either be blocked from his usage or the results will be reversed by the state. There are a lot of laws that sound revolutionary in liberal democracies, but he keeps talking as if the capitalist state is neutral and will simply let him use them liberally, maybe because he underestimates a local administration: it's waaay more constrained than territorial ones. Here in Barcelona we had the main street activist for affordable housing Ada Colau as a mayor for 8 years, she tried haaard, not only didn't she compensate the market's tendency, it actually got so much worse.
This is a weird illusion that would vanish if they looked closely at other leftist projects's "success" when ruling in liberal democracies, it's the sad eagerness of democratic leftists to get harder-faster-stronger results in order to convince voters in a system that surely sometimes conceded, like in your FDR's time, but nowadays simply makes sure that those results are tiny, never enough to keeping their voters encouraged, much less even dare compensate the tide of capitalism significantly.
Meanwhile, he'll be drowned in fake news from all buyable media (which most of his voter base follow) and fake legal accusations that the state will push as far as they can. They don't need him in jail, all they need is the thousands of "common sense" Dem casuals that vote for him to see him tarnished, put in the defensive, ugly, like another celebrity. I've seen relevant leftist politicians destroyed by fake accusations of covering their old ex who came up to be a pedophile. You'll see him grow 10 years old for every 4 of governance in exchange for poor results.
But the worst effect this process has is demobilizing leftists on a wider sense. It happened with Syriza in Greece and Podemos in Spain, because liberal democracy is still the main hope/cope for most leftists and when their rare successes fail miserably it drags them down for a decade, plummeting all wide working class organizing, specially unions.
That's why revolutionary communists sent their guys to liberal parliaments with reforms as a nice complement, but agitation as the main objective.
[I assume there's a lot of rationalization in this "analysis", I'm not that well read on marxism, please feel free to correct any overly opinionated take.]
Honestly I keep reading comments like these from cynical leftists but tbh they kind of fall flat in Mamdani's case bc he's said explicitly that the goal isn't to elect leftists but to build a movement to establish socialism and that elections are only a method to build that movement.
Defeatism is rampant in so many circles now. People are incapable of seeing anything as a win, even if it is small. "If he looks like he will win, he won't. If he does they will kill him. If they don't they will deport him. If they don't the something else bad will happen. And if all those things don't happen and he truly wins then he won't change anything anyway. And of it looks like he might then we will complain about him not being radical enough." There simply is no winning for so many western leftists.
They don't want to win. The sooner the western left is cast aside into the garbage the better.