In case you will upgrade management: Clients will be disconnected from MANAGEMENT ONLY, NOT from the gateways.
In case you will upgrade gateways: depending on gateway's current version, it might be possible that clients will be disconnected from upgraded GATEWAY. If management is connected behind same affected gateway, then also clients from management will be disconnected.
Please double-check drawings/topology what is in place to avoid surpises. Proper and up-to-date documentation is a key 😉
Kind regards,
Jozko Mrkvicka