Not only could we send those kinds of signals, we already have done it using the Arecibo Telescope (RIP), which h̶a̶s̶ had EIRPs ranging from 200 megawatts to 22,000,000 megawatts depending on the transmission frequency. In 1974, we beamed a short message to the Messier 13 globular cluster with a transmission power of just under half a megawatt.
https://en.wikipedia.org/wiki/Arecibo_message