Can you get a religious divorce without a civil one?

If a couple goes to a rabbi asking for a get, he will tell them to obtain a civil divorce first. I heard of a couple who wanted ONLY a religious divorce. The reason was that the husband had a medical condition and was dependent on his wife's health insurance (through her employer) and she was not willing to cut him loose. They parted amicably and wanted to be able to have relationships (no marriage, of course) without feeling they were committing adultery. I don't know how it ended. Would a rabbi accept to give a religious divorce without a civil one?