If you need a datapoint on how noisy those signals are: some people have combined a 144.6Mhz Raspberry Pi output with a narrow passive bandpass filter to generate a relatively clean and powerful 433MHz signal (the third harmonic, which is quite strong in a square wave): http://www.skagmo.com/page.php?p=projects/22_pihat
Recently I did a similar project in which a malicious hardware device leaks a victim's data (Password, credit card #, etc.) through a similar technique.
We used an FPGA though, so with a 100 Mhz fundamental frequency we had harmonics well into the 1.5 Ghz. We called it CPU-SDR. Video here:
Bonus: Using mutiple PCB traces, you have a basic Yagi-like directional antenna. Feeding different traces you can modify the RF radiation pattern it in real-time.
Yes, assuming there's strong harmonics (I'd be real surprised if there weren't), you should definitely put a bandpass filter between the Raspberry Pi and the antenna like these guys did.
Thanks for the link! That's a clever way of using harmonics to your advantage.