Good morning, Greg.
This is not a functionality of your stores bumping into each other. You would not get an error as such. If you have more than one store connecting at the exact same time - you will just get an error on HQ Mgr that one of the two stores 401 failed. You will then have to recreate the 401 by copying it and resending (copy because simply creating a new one will not capture the data from the dropped communication).
Regarding your connections schedule, with only 30 locations connecting maybe
1x before 11:00am, you are fine. I am sure you have mapped this out well.
I have not worked with stores connecting via a vpn, so I will not be of much help there. But, I do get the same thing you have every so often. It is usually something relating to Norton, or whatever free spywear the store thought would be fun to install that day.
I can see that you are using port 34200, and I am sure you have checked with the location. Is their test network successful? Have you asked them to export the log file so you can review it? I have a store with a messed up internal ID, and I did not know the error until they exported the log file.
If this is 1 of 30 with issues, really get your hands on this store (if possible) and see what is different about them. I would do this before it gets worse as time goes by.
Basically, I just did not want to see you get all side tracked by your connections schedule when that is not the issue. I have 83 stores connecting hourly.