It will insert restrictions, but "unnecessary" is debatable. If you are transmitting any sort of confidential information (credit cards, customer info, etc) then some sort of encrypted connection should be used.
Also, I apologize for misleading you on the SQL part, I didn't realize that you were using MySQL instead of MS SQL (though it is in your first post). That may not use 1433 or the dynamic port ranges that SQL uses. However, there are still security issues with leaving MySQL directly exposed.
Back to the problem, you say that these machines have a PC-based ethernet connection. Is it an actual PC running a commercially available OS inside the machine, or is it something else using PC hardware? If it's the former then you should be able to make an encrypted connection happen.
Another possibility would be to put the server behind the firewall in a DMZ and then forward the ports needed for MySQL to the server. If you go that route then you can use an firewall with stateful packet inspection and some sort of anti-malware capability to scan the traffic before it hits the database.