Hi cwkim,
I think you must have confused with the device offline and pool member forced offline terms.
When a pool member is set to forced offline state or disabled state, the monitoring does takes place on every interval. Even if a pool member is set to forced offline, that doesn't mean monitoring would stop for that member. Monitoring to a particular member would stop, only when the pool member is taken out of the pool.
What a forced offline means to a pool member ?
When set to Forced Offline, a node or pool member allows existing connections to time out, but no new connections are allowed.
What a disabled state means to a pool member ?
When set to Disabled, a node or pool member continues to process persistent and active connections. It can accept new connections only if the connections belong to an existing persistence session.
Now what a offline state means to a device ?
Force Offline is a maintenance operation that puts the BIG-IP system into an offline state; systems in this state do not pass traffic.
In simpler terms, a device put in offline state would not handle any traffic, it would break all connections that's there in it. Also no monitoring would take place.
Please go through the below articles if needed.
K13310: Disabling nodes or pool members for maintenance (11.x - 13.x)
K15122: Overview of the Force Offline option