Yes. And no I haven't tested it, although warned. I was thinking since I can whistle to about 2KHz and the tone passes on the receiver, why wouldn't two modem tones pass?
1. Are you sure it was your tone, with all imperfections? Not just the receiver or the network filling in what sounds enough like your tone to be pleasing to the ear, according to the models and assumptions baked into the GSM suite?
2. FM, and the degenerate form known as FSK, generates a well-characterized, mathematically infinite series of sidebands, which also need to be passed through the channel in order to reconstruct the signal on the far end. Some of those sidebands will be modified or dropped by the speech model during compression because the ear will not perceive them.
3. At the bare minimum, synthesize some modem tones and pass them through the channel, record the result, and analyze what's left in the frequency domain. You can try GNU Radio Companion as a flow-graph-based signal processing workbench, if you don't have access to Matlab. To start, switch between mark and space tones every 10 bit times, then progressively reduce the number of bits.
4. If you don't want to do that, play music through the phones and compare the original program to the transmitted program. To minimize your brain filling in the blanks, play a selection you're familiar with, then follow with an unfamiliar selection.