I couldn’t figure out if machines that are joined to the main ArcGIS Server machine function as “stand-by” machine such that they do respond just in case the main ArcGIS Server Machine fails. Or otherwise, they do share their resources with the main machines to respond the requests.
Any help is highly appreciated
Here is a link to the documentation (Join an existing site), hopefully this can shed some light on your question.
As the documentation states, "The Join Site operation adds a new machine to an existing ArcGIS Server site. This can be done temporarily to migrate to new machines, or more permanently to increase the resources and processing power of your server site".
Hopefully this helps.
All ArcGIS Server machines are "peers" of each other and are added to increase resources to handle load, provide high availability, migrate to new machines etc. There is no concept of "standby" for the machines that are part of an ArcGIS Server site. You would need the ArcGIS Web Adaptor or some other Load Balancer/Reverse Proxy set up so requests can be distributed across the machines in the site.