The Pi can generate a square wave, and AFAIK, plenty of harmonics to go with that square wave.
You are likely going to want (and need IMO) a bandpass filter between the output and antenna.
I have no real idea of the output impedance at the Pi connection, but given the low power, I would not be too concerned about closely matching it. Given the few mWs of power contrasted against feedline and matching losses, I would look at placing the Pi and filter as close to or even right at the transmitting antenna feedpoint if possible.