Usually with OS units, the transmitter is on a separate daughter board with typically 4 connections: ground, power, enable and data. The data line is going to run around a kHz or so. Of course if you see stuff on the data line there's no guarantee that the transmitter is actually working but it would be encouraging...
Since you're a ham...you can make a coil from a few turns of magnet or hookup wire and connect to an RF or microwave signal diode and R-C detector (time constant of maybe 100us or so) -- then connect that to the sound card input on your PC. If you place the coil right next to the anemometer tx antenna you'll hear something on the sound card if the tx is working. It does need to be like really CLOSE to the tx antenna though. I've hooked the coil up to a cable TV amplifier and then put the diode detector on the amplifier output and that has worked well.