I don't believe time of submission makes any difference. Here's what happened with ours. I attempted to use the original process submitting our applications from the US on 16 Aug. Received nothing but the auto response that they were working on it. Flew to Switzerland 27 Aug and about a week later got an email saying they were giving up on that process and to use the FranceConnect outfit. Thankfully, I had saved all the original attachments to a thumb drive and brought it with me. On 10 Sep while in Lucerne at about 2 in the afternoon I used a PC at our hotel and set up an acct with FranceConnect then submitted my new application. They sent an email saying it had been received but not processed. Also asked did I want to submit another which I did for my husband answering all the questions the same way though with his info. Logged off the computer and went upstairs. By they time I got there I'd received emails that his had been received, then that it was being processed and then the actual approval and QR code - ALL within about 3 minutes.
The next morning - also during European business hours I used their message feature to ask about mine. No response. Tried again about a week later with the same results. Nothing until Sep when I got the email that it was being processed then a minute later that it had been approved with my QR code. I looked at the actual time stamps of the email and they are exactly 1 minute apart. No human could have read thru all the answers and checked the attachments in that time frame.
Coincidentally (or not) that was the morning our group had taken our covid tests for our return flights on the 24th. Was there something about the tech entering the results that triggered this? I have no idea. But given what I went through I don't think time of day has any impact nor that an actual human being has much if any involvement in this process. Though for a computer process it's pretty darn inefficient and/or random.
Fortunately, I never had an instance during 2 weeks in France where I needed anything but my CDC card. We started at Versailles, went thru the Loire valley, Brittany, Normandy and finally Paris. Most restaurants and tour sites asked for it and I only once heard of someone in our group where a restaurant wouldn't accept it.