I don't think so, but maybe she would because she won the popular vote.
I don't think she would want to even try unless she thought that she would win. It would be humiliated for her if she lost either the nomination or the election.
Stevenson was a last minute drafted candidate in 1952, and the party pushed him in 1956 knowing he would lose. Stevenson believed he'd be the Democratic nominee in 1960, and it wasn't an unreasonable belief.
If you look at the candidates that were nominated twice after losing, you have Nixon (R), Dewey (R), and Bryan (D). They're the only ones. If you want to talk about folks who ran twice but were nominated and lost, there are a number of folks here, but the list has a lot of qualifiers. Reagan ran twice and lost before going all the way. McGovern ran once after losing, and he ran in 1968 at the last minute. McCain and Romney are recent examples, and Bob Dole was nominated after running twice before and being a VP nominee (and being considered a negative at that).
Let's look at why the two-time nominees were in that position. Dewey was young, and a real comer who did fairly well against FDR in 1944, given the state of the party at that time. Stevenson's been covered. Nixon was a former VP who served under a President who had a massive heart attack in office and almost won the Presidency in 1960. Bryan was the leader of the strongest faction of the Democratic Party, holding sway in the South and West; the only year he wasn't nominated was a year where conservatives nominated Alton B. Parker and Progressives were happy with TR.
One thing Hillary would have going for her if she ran in 2020 is that she, like Dewey, Stevenson, Nixon, and Bryan, ran at a time where their party was low on prominent leaders. The most prominent Democrats, other than Hillary, are Biden and Gore, and both of them are old. There's really no on the horizon that looks to be the future leader of the Democratic Party's Presidential wing. (The Kamala Harris threads are a joke, to be honest.) She's who she is, and if the last roud of scandals fade to the point where folks view them as phony and trumped-up (no pun intended), then Americans might view her as someone that's "owed" the job.
All of that, and that's a lot, would have to be balanced against (A) the anger donors have over such a "sure thing" not coming through, (B) her consistent tendency toward dishonest secretiveness that erodes her trust, and (C) the fact that folks just don't like her. Hillary caused the gender gap to work AGAINST her, and it's because of her persona, and not her gender. She'd like to run again, and it'll be talked about. But I really don't see the big money donors getting behind her. If someone's going to be a two-time nominee in 2020, it'll be Al Gore.
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