While applying a client setting requires an action, there is no impact to the client. No reboots, etc.
You can either select individual clients and push out the setting but obviously some can get missed especially in larger and diverse environments.
I would recommend the value be dynamically generated. As an example, which I highlighted in a recent thread (Separate Dev, Test & Prod as Automatic Groups Options - #6 by MatthiasW), it’s possible to add a .JSON file to a site that is then distributed to all clients. Next have an open policy action that is created by a task that uses a combination of relevance and actionscript to set the value from that .JSON file. If a value is not found in the file, you can then choose a default option so that you are sure ALL clients have a value.
Plenty of ways to do it, so have to dig in a bit with an engineers hat to see what works for your org/team.