Radio with crystal oscillator
No. It's not an oscillator, it's just a crystal. You'll have to build an oscillator with it yourself, which only requires a few components, for instance like this one with a FET:  



If you don't want to build the oscillator yourself you can also buy them for a few dollars. Then you don't have to worry about stability and such.



The oscillator won't give you enough power to drive a 50 &Omega; antenna, but an HF amplifier following the oscillator will do the job.   

edit
That gives you a "radio", but it just transmits a fixed sine wave(*), your 20 MHz carrier, no signal. For FM or PM you'll have to modulate the oscillator's frequency. AM can be done at the amplifier stage. CW (Continuous Wave) for instance just switches the carrier on and off.

(*) The encased oscillator shown outputs a digital square wave, so you'll have to filter that, otherwise you'll transmit 20 MHz, 60 MHz, 100 MHz, etc.