No, our radio emissions would not be trivially detectable. In fact they would be phenomenally difficult to detect even from our nearest stellar neighbor, Proxima Centauri. If you take the most powerful BBC antenna [1], then a James Webb-sized telescope placed near Proxima Centauri, and pointing straight at the Earth would receive less than 5 photons per second from that antenna.

Here's the calculation, in case you're curious: one light year is about 10^16 meters; a sphere of radius 4.25 ly has an area of 2 10^34 m2. The BBC antenna emits in the 200 kHz band, so a single photon has an energy of (plank const) x (frequency) = (6.6 10^-34) x (200 10^3) = 1.3 10^-28. The antenna has a power of 500 kW, so that translates into 3.8 10^33 photons per second. That means at Proxima's distance each square meter will be crossed by a photon about once every 5.4 seconds. The James Webb telescope has a receiving area of 25 m2, so you end up with a bit less than 5 photons per second.

[1] https://en.wikipedia.org/wiki/Droitwich_Transmitting_Station