Uh, no. Range is not a function of signal power. It more is a function of the overall signal/noise ratio and the sensitivity of the receiver. This includes noise introduced in the transmitter, natural/other noise, and noise introduced in the receiver. An antenna system with gain can both concentrate and attenuate signals, depending on the directivity and where its pointed.
BTW, I got over 1400 miles out of a little 0.3 watt ham signal, but thats no where near as impressive as Earth still being able to receive signals from Voyager 1 and 2 nearly 10 billion miles away. That's impressive.
If you're not careful, you're going to catch something.