I have set a global parameter critical (type: boolean, value: true) and created hosts with this parameter enabled. After creating the hosts, I confirmed that the parameter appears on the host settings page.

Next, I attempted to search for hosts carrying the critical parameter on the “All Hosts” page using the following queries in the search field:

params_name = critical
params_name ~ critical

Result:

the host is not listed.

This works for at least host and hostgroup parameters.