A short answer is not really.
An audio amplifier can respond to frequencies from 20 Hz to 20 kHz and when connected with a speaker, the coil in the speaker resonates as per the output frequency and if that can be connected to a loop antenna instead, it should radiate radio waves too.
The coil in the loudspeaker is not resonating with anything, at least that is not the intended or desired behavior, to produce acoustic vibrations. Resonance is often a "magic" word, which leads to a lot of specious statements, so please be careful with that word. If you can't explain the behavior without using that word, it deserves a critical review.
If you use a large enough loop, you can produce a magnetic field of the audio signal. However, that is just that, the magnetic field. The field dies off inversely proportional to the distance squared. That will not lead to a radio signal or electromagnetic wave that propagates which requires both magnetic and electric fields.
Those local magnetic fields were used in the past in wireless guidance devices (used in museums, etc.). Each room had different loops to induce the magnetic field. I'm not sure if those are still in use somewhere, but most likely, virtually all have been replaced by networked or storage-based devices by now.
I said "not really," and not "exactly no." If you study WWVB transmitter site in Fort Collins, CO and its antenna, you know what it takes to transmit 60kHz signal. Some other standard time broadcasts (e.g., JJY of Japan) use 40kHz in addition to 60kHz. So, 40 kHz is the lowest radio frequency commonly used (and I know of). German DCF77 in Mainflingen uses 77.5kHz despite having a bigger land than Japan. (I think there was 20-30kHz broadcast station in Sweden that went QRT fairly recently. Submarines also use very low frequencies with towed antennae in the water.) Anyway, those are the lowest commonly used frequencies, and you can study their antenna to appreciate what it takes to transmit at those frequencies. If you have a lot of land, you could presumably transmit at the top of the audio amplifier's frequency range, but you would still require a license, but that certainly won't be an amateur radio license.
Your tape recorder experience is actually something else. You were receiving some 1MHz radio signal, probably on the order of 100uV to 10mV range depending on the field strength, which was AM detected (rectified) by the transistor used to amplify and equalize very weak signals coming out of the playback magnetic head.
Now, this is also something else. If you used a class-D amplifier, especially if the amp omits the output LPF or you modified/removed it and fed a large enough antenna, you can actually transmit long/medium/short wave radio. That is because class-D operates by switching mode, and the switching frequency and its harmonics serve as carriers. The receiving end requires a detector to demodulate the audio signal. I would expect the demodulated signal to be heavily distorted because of the way class-D works. Caveat: You'll need a high-pass filter and impedance matching so that you don't blow the amplifier. Also, this is illegal. Just keep it to your conceptual simulation.
This is also something else, but peripherally related. There are JJY/WWVB emulator apps that run on tablets and smartphones. Those produce an audio frequency carrier one of whose harmonics come to 40kHz or 60kHz, modulated by the time code. The magnetic field (not radio wave) created by the loudspeaker is picked up by the radio-synched clock placed right next to it to automatically set the date/time where the JJY/WWVB signal is weak (such as US northeast).