Yes. They would be required to provide full refunds to customers for any reason.
According to the Federal Trade Commission:
regardless of the price of the product, advertising terms such as "satisfaction guaranteed" or "money back guarantee" should be used only if the advertiser is willing to provide full refunds to customers when, for any reason, they return the merchandise.
It could also mean, in other circumstances, that you would be compensated for losses caused by your purchase. For instance, if a dry cleaner lost your pants, they would likely have to additionally compensate you for the cost of replacing said pants.
That said, that doesn't mean that the customer is untitled to unlimited compensation for claimed or perceived loss until they are satisfied. For instance, to use one of my favorite lawsuits as an example, a customer would not be entitled to $54 million for the loss of their pants, as a now-former judge once claimed in a lawsuit. In discussing why a customer would not be entitled to that, the District of Columbia Court of Appeals cites various cases as examples of how such a guarantee should be interpreted. Note that this case is under District of Columbia law, but the principles (especially relating to common law fraud) are pretty similar. The Court notes that:
as with a common law fraud claim, a claim of an unfair trade practice is properly considered in terms of how the practice would be viewed and understood by a reasonable consumer
and gives as a particularly relevant example:
although a television set had been guaranteed to the “personal satisfaction” of the purchaser at the time of purchase, the customer could not return the television for a refund over fifteen months after it was purchased
While the refund period is probably not unlimited for that reason, the FTC does recommend that a merchant wishing to impose a specific time restriction disclose that or any other conditions on the offer:
an ad mentioning a satisfaction guarantee or similar offer should inform consumers of any material conditions or limitations on the offer. For example, a restriction on the offer to a specific time period, such as 30 days, is a material condition that should be disclosed.