Yes you can page handsets and it depends on how many you want to page at one time.
You don't say what system type or software level or how many you want to page.
As for scheduling this is not possible.
Here is a list
Up to 16 page groups are supported by the system. Each group can have up to 250 members with a maximum of
16 IP Phones with the CX or CXi Controller
32 IP Phones with the 100 User, 250 User, or MX Controller
32 IP Phones with the MXe
64 IP Phones with the MXe expanded
64 IP Phones with the AX Controller
64 IP Phones with the MXe Server
64 IP Phones with the 700 User or LX Controller.
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