I haven't tried it, mostly because I wanted to mix manual input with arduino input... including with some mixing done by the radio.
As far as I know, your idea should work because the HF module takes the unmodulated pulse series as input and just modulates it by the carrier wave. IOW, yes, you should be able to hook the arduino straight to the HF module for the win.
I, unfortunately, am too chicken to try it with my HF modules as they are rather pricey, and require some add'l interaction to set the carrier frequency (synth modules, not crystal). If I can get my hands on an inexpensive toy with radio included, I'll give it a shot!