There's a very small chance of it working (and I don't think it's a very realistic one but then again no one counting on Henry Tudor winning). If someone like Henry Tudor isn't there (one of the last who could carry the Lancaster banner) or if Richard's continues to have more troubles or dies without a son. A Kingmaker may be able to make it happen (especially if he has a son). What if she marries a foreign monarch, and they win and rule as joint rulers? At the very least if Richard continues to reign, she could be the focus of plots. A generation before, as a child Margaret Beaufort was apparently a center of a plot with John de la Pole wanting to make her and his son (technically her current husband) monarchs. Who knows what Elizabeth and her sisters really thought about the possibilities about it or whether it was her right by blood?
Without meaning to sound sexist, they were women and didn't consider it something to aim for. Remember that Edward IV had two sons - brothers of Elizabeth - who only died young because their uncle, Edward's brother, had them kidnapped and murdered so that he could take the throne, so Elizabeth wasn't even in a strong position until her chance had gone. It was very uncommon for a woman to actually manage to get to the front of the queue, so all except the most intensely manipulative women simply didn't try to promote their interests, and focused instead on persuading their father or brother to pair them up with a dashing and important Prince so that their children could grow up to be everything that, as women, they couldn't be. It's not exactly politically correct, but it's how it was.
And marrying a foreign monarch is really not the way to go. The 18th century kind of glamourised Personal Unions in the 21st century reader's eye, but Personal Unions were viewed as a terrifying possibility for a country in this era (and as a useless waste of time in the 18th century). People didn't want Personal Unions as you could only have one monarch for two territories, which meant that somewhere along the way, one or more likely both countries were going to get sacrificed for the advancement of others. The nobility would become less powerful because of having to share their monarch's attention with the nobility from the other state, the middle classes felt that the King would pursue an economic strategy that favoured either random monopolies or a great-in-theory-rubbish-in-practise system to combine the economies of both countries at the expense of the traditionally strong guilds and the powerful of the town councils, and the peasants frequently suffered when their monarch went abroad to the other Kingdom and stopped paying attention to the plight of the common man back home (remember that this is an era when even a lowly serf could petition the King for redress...but only if the King was close by).
In short, if Elizabeth were to marry a foreign monarch, the foreign monarch might support her because of seeing money symbols in his eyes, but she would lose all support back in England because no-one in England would want to be shackled to another country.