can iRule work without assigning it to any virtual server ?

to check if your irule is assigned to a virtual server, you can use this command in tmsh

list ltm virtual one-line | grep YourIRuleName

it will display only virtual servers which contains the irule name in the configuration.

If you have irules not assigned to any virtual server, it is not enabled, except the RULE_INIT event which is executed when you load it (or reboot the system) and can change static variables.

Static variables are shared in the whole system, if static variables names are the same in multiple irules, the last irule loaded set the variable value.