If your question is if the license can make the marriage effective as of the date of the chasuna, legally per the laws of the State, the answer to that depends on the law of whichever State you are marrying in. In New York and most States, you need to get the license prior to the marriage. In New York you need to get the license at least 24 hours before the marriage. The license is then valid to get married within 60 days from when the license was issued.
If you didn’t get the State marriage license prior to the marriage ceremony, you will need to use a later date (i.e. after the license was obtained) as the official date you got married under State law.
If your question is whether your kiddushin is valid if you do not get a marriage license, it is 100% valid and you are unquestionably halachicly married even if you never get a State marriage license.
If your question is whether State law requires you to obtain a marriage license if you get married under religious law, the answer is no. You are legally entitled to get married under religious law (i.e. chupa v’kiddushin) and choose to not get a State marriage license.
Some (but not all) States will consider you legally married if you marry under religious law, and reside together with your spouse, even if you never get a State marriage license.