Yes. So long as you have a subscription service (or are willing to eat the cost). This is how many home security systems handle things these days. No need for a phone line (which can be cut) or wifi (which is lost with a power outage). A control panel and the sensors have batteries that continue operating despite power loss and network outages.

A powerful use case here is at-home medical devices (think blood glucose monitors). With a SIM and cellular service, they can work anywhere, be agnostic to consumer WiFi issues (oops, someone changed the WiFi password!), and give "real-time" updates to a doctor or other health professional. Getting patient data has a huge barrier today and there is a ton of room for improvement, leaving the door open to better/more proactive care.

Potentially yes. This is just a SIM card, so one would additionally need to have a modem, consistent power source and space for all of these extra items. The value of the telemetry would need to be worth several dollars / month over several years to justify this.