1, Each state is different.
2. In some cases, the government won’t recognize a marriage without the license. In some cases, the marriage is recognized but the clergyman is subject to a fine.
3. In some cases, the marriage is recognized with or without the license (meaning that a frum religious wedding is considered a valid civil marriage regardless of whether there is a wedding, even if the parties desire that their marriage not be recognized by the government, e.g. if they want a kosher marriage but wish to keep filing as single for tax purposes).
4. Some states have “common law marriage”, meaning any sort of public statement that you are getting married is probably recognized as creating a valid marriage.
5, It is very hard to get a marriage recognized if you don’t bother with the license, even if technically the marriage is valid. This can be a problem in one spouse wants to include the other (and the children) in health care, it affects taxes and social security, it affect custody in the event of a divorce or death. In lieu of getting a license, you might at some point need to hire a lawyer and get a court order to prove the marriage, and you might be prosecuted for tax fraud filing a joint return or lose custody of one’s children to the state. Better to get the license.