I don’t think it’s terribly clear, but the general answer should be “yes.” A injunction (particularly a preliminary injunction) does not enjoin “a law”. A court has no ability to “strike down” a law and the law remains unless and until repealed by the legislature. The court enjoins certain individuals (usually executive branch officials) from enforcing a law.
I think that the generally rule is that, if the final judgment dissolves the injunction, the state court prosecute any violation that occurs, subject to the limitations period.
However, I thought the point of an injunction was to prevent irreparable harm from occurring before the case can be decided by the court.
So, if my business is widget sales and I can be prosecuted for selling widgets while the injunction is in place (assuming the law is upheld), the harm is still done. Unless I want to take the risk of going to jail (probably not) I need to stop selling widgets. Given how long these cases can take that would quite likely put me out of business.