Maybe, but I think the reports of a Democratic schism are greatly exaggerated. For example, we won't have some Bernie bro turfing out Senators like McCaskill and Heitkamp for being too moderate and then losing the general in a landslide. It might happen in some safe-D districts, but the Democrats have more of a spectrum of beliefs, rather than several discrete and competing groups like the Republicans have with the religious right, business conservatives, Paulites, Trumpists, etc.
Yes, this is why I don't think there'll be a leftist Tea Party for those reasons you outlined. Democrats are (or at least claim to be) a big tent party where liberals, moderates, and conservatives are welcomed. Remember that the Tea Party cost Republicans the Senate majority in 2010 when nutjobs like O'Donnell, Angle, and Buck were nominated (and in 2012 also with Todd Akin and Richard Mourdock). They don't need to be out there engaging in Berniebot tactics and going against moderate/conservative/jfern-like "neoliberal warmongering corporatist" red state Democrats only to have them lose the primary and then the Republican candidate handily win those seats. The Tea Party was more united in their hatred of Obama and "hands off my health care," which motivated them to turn out and vote.