Can a radio transmitter somehow detect the number of receivers in its area?
Actually, yes, a receiver can affect the transmitter. Passive RFID is based on this principle.

However, RFID only works at very close distances, where the receiver is absorbing something on the order of 10-4 to 10-5 of the transmitter's signal. In other words, the transmitter is sending out hundreds of milliwatts, while the receiver is absorbing a few microwatts. Such changes are just barely detectable at the transmitter with careful techniques.

However, for general broadcast radio, the transmitter is sending out tens to hundreds of kilowatts, while the receiver is absorbing tens to hundreds of femtowatts, which is a fraction on the order of 10-18. This is completely undetectable at the transmitter. Furthermore, receivers absorb signal regardless of whether they're turned on or not, so even if it were detectable, it would tell you nothing about how many people were actually listening.