I am bombarded with ads on Facebook for the Sense. This
    device allows you to monitor whole-home power
    consumption. ... I realized it would be extremely simple
    to do something similar without any wires or hassle.

Sense monitors two things:

* instantaneous current

* instantaneous voltage

Different devices have different electrical signatures, and this allows it to learn what devices you have in your house. RTL-SDR is much too low-resolution for this.

RTL-SDR monitoring would actually be awesome to add to Sense: the method it uses for measuring current is designed for microsecond-level accuracy, not long-term accuracy like your meter. So over time they won't keep perfectly in sync. If Sense could automatically read your meter it could calibrate itself.