Yes. I'm prepared to do a lot of experimentation. Here's a guy that makes a train horn of pvc pipes and joints:
I'd have to place the solenoid and the ring inside the cup, pushing the membrane from behind (seen at video 2:10).
So it's probably ok to run variable current through the solenoid just to create a force rather than a movement. The full movement or throw of a solenoid plunger might be some 15 mm but the membrane might let it move only 2-3 mm at full force. I guess that's ok for the solenoid. I mean, it's just a coil and the same current runs through it no matter if the plunger moves all 15 mm or if it is restricted by a counter force. It's not like an electric motor, which might burn its coils, if it can't rotate freely while loaded with a voltage.
Experimentation would include determining the force needed to raise the pitch of the vibrating membrane say two octaves (which is pretty much for a trumpetist). Then choosing the right solenoid that could create that force with 5 V (or 12 V or whatever I have to use). And after building the cup with the solenoid and everything (except the horn-bell), I'd have to build a circuit with one potentiometer controlling the solenoid force and another potentiometer controlling the supplied air pressure. The solenoid force determines the pitch or the frequency of the vibrating membrane. The air pressure controls the quality of the produced sound (too low pressure - no sound at all, too high pressure - too much air in the sound). When this is accomplished, I'll have a table containing the solenoid values and the air pressure values for each desired tone.
Since the length of the horn kind of determines the pitch, I should be able to vary the length of the horn, too, not only the tension of the membrane and the pressure of the supplied air. For this I'd attach a real trumpet (or any other brass instrument) to the cup. Then I'd need three more solenoids to push the valves of the trumpet.