It's certainly a State-specific question. I think the litmus test is how the public can verify licensure. Maybe some States require written evidence that must be produced on demand (I'm thinking a license card or some certificate), but I'd imagine most (Oregon, for one) simply offer two ways of verification: website lookup and written query. So...
If you have written evidence (card or some certificate), have at.
If you are listed on website lookup, have at.
If you receive a written query, have at.
Simply tying your name to a license number seems insufficient to me.
I agree with Raanne that the test is not the final requirement in some States, even if for many it is.
Oh, yeah... and did I say CONGRATULATIONS?!? What a feeling, eh? Where are you going to get your stamp from?