From my experience (which is probably out of date)
The person on the desk will have made a record of everything you said,
as long as you explained that you had been in the previous day but they had closed early
it will probably go through the preliminary stages of going to court, but will be dropped before it actually gets there. The statement from the desk clerk will be seen by the cps (or whoever it is that oversees these things) and you will be notified that they are taking no further action. If it does go as far as a hearing it will be thrown out, but you would still need to attend.
This is dependant on your documents being in order.
Don't take any of this as gospel though, at the end of the day you can prove they closed early and that gives you mitigation for not presenting your documents.
They could take this to the Nth degree if they choose to, but it's unlikely.
Axe