It would actually depend on which way the film was going,
If they have the movie take place before Steve was frozen, then she would be needed yet.
If they had Steve unfrozen it would then depend on whether or not he had a secret identity.
if Steve is unfrozen and is known by everyone, lives in SHIELD (or the Avengers mansion), and only associates with other heroes and SHIELD and government agents, then she would probably never come into the picture.
But
If Steve has a life outside of SHIELD, the Avengers, and Captain America, like if his identity was secret, then Steve could have an apartment in New York, work as a comic book artist, and have friends like Bernie Rosenthal and the other neighbors he had during that run.
(personally I am torn. If you have his ID secret then you loose the chance to make him different from other superhero movies. making him more of a public servant or a Government agent than a superhero. But if you make his ID known then you loose the chance to have him have this separate and interesting life as a comic artist and friends with these interesting people.)
I don't know who would be cast for the role, but maybe I can think up some.
More pics of Bernie:
