Clare, the license requirements are separate. Other states don't care how plants arrive; they still want their laws complied with. I think you're plants should be safe but I know when I checked with Florida even leafless pomegranate scions were required to have a snail certificate. Richard said his county has a program for snails and slugs so his officials have said he's okay to ship without but I think that's a special situation. California also has strict requirements for things coming in but the requirement for what I'm talking about is what Florida requires from California shippers. California also wants you to have a nursery license but there are many who go without. It's a hassle, ask Tony. He waits months for someone to come inspect and clear him to sell.
Here is where folks can find summaries of laws for various states in the U.S.
National Plant Board - Laws and Regulations