Clients need to match. You cannot use a down rev client with an updated server.
I don't think you can use an updated client with a down rev server either.
You do NOT want people connecting while you're upgrading.
Schedule the downtime.
Lock the vault.
Upgrade the server.
Upgrade the clients.
No one will be connecting during the upgrade but I'm in the US and we have a couple laptop clients in Europe whom I won't be able to upgrade until about noon their time. Thanks for the confirmation.
As a side note, you CAN use an older version of SolidWorks with newer EPDM, which I think is what you heard of before. But Brian is correct that you have to have a matching EPDM Client to the EPDM Server version (Same SP and everything).