The usual danger is the the AC circuit looks "benign" --- but as soon a you touch it, the inverter goes into action increasing the amperage acroos as it "kicks out" of standby.

You just need to assume that ALL AC lines that it serves are assumed as HOT unless i) you remove the AC source; AND ii) you disconnect the inverter completely from the circuit by a switch, or better yet, disconnecting the DC power to the inverter.