I have not cycled in Patagonia, but I was there in 05 (before I became a cyclist). We spent time at Torres del Paine which is absolutely gorgeous. There are lots of hostel type places to stay inside the park, and camping is highly restricted due to the sensitive land. I think you would love a cycling trip here, we saw two cyclists who were just setting out but we thought it looked incredible. Of course, that is in no small part due to the scenery.
One note, a lot of the roads in the area we were were not paved. Something to keep in mind.