No. Even if he protected it later, the tenancy start date is the key date.
Remember he also has an obligation to let you know that it's been protected. This is probably just as important as whether it has actually been protected or not. So check your paperwork and any emails from him.
Like I said before, not all of the deposit schemes send emails to the tenant. I have had two tenancies in the last three years that did not automatically generate emails, but the agent emailed me a certificate, and when I checked the scheme online, it was legit, the deposit was there.
Given that he doesn't even have a rent review clause in your contract, I doubt he's done it. I have never had one without one, even if all it says is 'rent will be reviewed annually.'
But, if you want peace of mind, change the tenancy date to every day after the start date plus thirty days, and see if anything comes up in any of them.
My next piece of advice is that the best time to get Shelter on the phone is 8.01am, just after their lines open, and before most office workers settle in at around 9am.