Probably, but there are a catalogue of ifs: if he is straightforward and composed in his denial of the claims of harassment; if the women don’t come forward and put a compelling face on the charges, and if this is not just the tip of the iceberg around claims as to how he treats women under his supervision.
The Cain team needs to study up on some recent history: how effectively the McCain campaign handled a New York Times story hinting at his infidelity with a lobbyist, and how Gov. Nikki Haley fended off even more lurid allegations in South Carolina last year.
McCain and Haley both understood that the Republican base distrusts these kinds of blows as a political hit job, and Cain is already stoking the same flames.
Finally, it should also be said that for a candidate whose ceiling was already about where he is today, “survival” is a relative term.