Can I use the Smart Plug to monitor my refrigerator or freezer?

In most situations you can monitor your refrigerator or freezer using the Emporia Smart Plug as long as it's within the Smart Plug's limitations (link below) without issue.

As with all smart home appliances, it can have some odd behavior due to device resetting or more. If you're managing appliance usage remotely (such as your vacation, beach or rental house), and you're not on location every day; it might be possible for the Smart Plug to be turned off without direct notification or alerts for your side. In these situations we'd recommend caution to ensure you don't lose power for any critical loads where a loss of power for an extended amount of time might cause problems.

So as long as you can access the plug to reset it or reconnect it to the WiFi, there is should be no problem.

Plugs limitations can be found here.