Can I switch to SAT with Essay on test day?

I mistakenly registered for just the SAT instead of the SAT with Essay. I didn't realize this until my test date, so I talked to the supervisor and he gave me permission to write the essay.

Should I be worried that my test won't be scored because my registration doesn't match what I actually took?

You are allowed to switch from the SAT to the SAT with Essay if your test supervisor okays it (without a change fee), as long as you pay the College Board the price difference between the two tests. Since your test supervisor gave you permission to take the SAT with essay, the only reason your test wouldn't be scored is if you neglected to pay the price difference of $12.