I guess it depends on what you mean by "version of trump."
- A cult-of-personality candidate can win with Dems. Obama and Clinton both hit that note pretty well for their zeitgeist.
- A celebrity that knows memes and doesn't have a political history to base attacks off? I generally don't think would work, but it's iffy. Familiarity is a big variable that helps candidates (this applies to Biden and Bernie even). There are other arbitrary variables that are surprisingly correlated to more electoral success (body types and shyt). So maybe if the Rock and Kevin Hart meme hard enough, party mechanisms can be overcome (like with Trump). I'm skeptical it could go that far, but I didn't think Trump could win either. Celebrities would get a lot of free press.
- Would unadulterated shyt talk succeed? Idk...Hard to imagine that going over as well on a Democratic debate stage. Bill Burr roasting Pete and Kamala on the debate stage would be funny though. It has worked elsewhere though with fed up electorates. I remember a tv-comedian winning a presidential election for a euro-country with a similar "I'm funny, vague about my politics, and left-leaning" but turning out to be a disappointment. I think it was Ukraine (because Trump tried to strongarm him in the phone call and sparked the first impeachment hearings). So there's some basis for it working at a big scale.
- But an additional note. A lot of times this sort of vague about issues, but charismatic on rhetoric politics turns out to just be a guise for the worst types. Trump is celebrated by his party precisely because conservatives have certain authoritarian leanings. That type of approach from leftist promises can be a similar type of power grab where they just oust actual lefties and turn out pretty fascist.
And also...The Democratic party is pretty much modeled on a "I waited my turn" kinda thing. Obama was able to break that, but it's why Clinton kept trying. It's why Rahm Emanuel just HAD to get some kinda appointment. It'll be why they force-feed candidates that proved completely mediocre last primaries as the front-runners this time. There's machinery in place to block upstarts like Trump from happening in the Dems (remember the super-delegate drama?). So it's tougher to have a left version of Trump for all sorts of reasons, and possibly the biggest is that the party has been built to insulate power.