Broadly speaking, I see two possibilities. First, these women might lift Biden into office, decide their work is done, and let their organizations fall apart. This is basically what happened in 2009 after Obama took office and deliberately destroyed the vast Obama for America organizing structure that had won him the primary and the general election. Alternatively, these groups could stay the course, and continue organizing to push Biden to deliver on his promises or to achieve other goals.
It is, of course, impossible to predict the future with any confidence at such a chaotic time. (Trump might win, in which case these women will surely stay in politics.) It might indeed turn out that getting rid of Trump will be such a profound relief that people will just quit and go back to brunch.
However, there are some reasons to suspect otherwise. For one thing, liberals do not love Biden to nearly the same degree as they love Barack Obama. Biden has a relatively low “very unfavorable” rating, but he also has a low “very favorable” rating — in other words, even dedicated Democrats have fairly mild feelings about him. In the primary, he was clearly who loyal Democrats thought was likeliest to beat Trump, rather than someone who captured their hearts. Organization-wise, that is a good thing, because it means rank-and-file liberals will be more resistant to any Obama-style messages to go home and let the party elites handle everything, and less likely to think the job is finished with the success of a single candidate.