Having had a look at the new Inspector's Handbook, what I just said may not be true anymore. You do still have to be approved to take the written test but the guidance only says the authorization must be dated to expire on the same date that the applicant's medical will expire.
The reg (61.153(e)) just says that applicant must meet the experience requirements before applying for the flight test. Don't know why that would be there if you had to prove your times before the written.