No. Sal Hepatica was so named because it was supposed to be a natural laxative salt that was beneficial to the liver, similar to another popular patent medicine of its time, Carter's Little Liver Pills. "Hepatic" means "related to the liver". Bristol Myers discontinued Sal Hepatica because it was being investigated by the FTC the same way the Carter's was (see the 1951 Time article); when the Supreme Court refused to take Carter's case (and Carter's had to drop any reference to "Liver" from its name), "Sal Hepatica" just became an effervescent laxative.
As you can see from the Sal Hepatica label, "liverwort" wasn't an ingredient:
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