You cannot power the Sense from USB or otherwise from outside the panel and keep it within US electrical code. This is a device that is built to be inside your electrical panel and there are loads of rules to prevent what you are suggesting. And before you say “then put a USB power brice inside the panel”, that is also not ok without severe modification to your panel.
If Sense built a device that was designed to ONLY live outside your panel, then maybe they could do such a thing but the question is why. If the home is without power, there is nothing for it to report. If the home has a deep enough brownout for the Sense to drop offline, then again, there isn’t anything for it to monitor.
You say “the whole idea is for Sense to be able to detect brown outs”. I have never heard this claim before on these forums not in their marketing. The whole idea is to be able to monitor power usage of devices in your home. Power quality monitoring or even voltage monitoring is not something I believe Sense has ever claimed to monitor. Sure you can see voltage on once screen, but monitoring said voltage is not a feature of the device.
Alerts - As mentioned by @waterboysh, the watchdog for a device being offline is not instant.
And as @ixu said, the alert does not come from the monitor, but from the cloud. There is no way for it to come from the monitor. The Sense monitor doesn’t know its going to lose power, so it can’t send an alert saying that it is going to lose power. Also, the alert is not “your device has lost power”. it is “your device has gone offline”. You will get the same alert if your internet drops out and the Sense servers don’t get a response. All they know is that the Sense hasn’t dialed home in over 30 minutes.