Could you do the colorado bike tour on a hard tail with road tires. Yes, a lot of people rode different types of bikes like that. I myself really like a road bike for riding the road, a mountain bike for offroad, etc. They are designed for the activity and road bikes are so fun once you get used to them!

I would recommend a triple chain ring or a compact for a road bike tho. I have just a regular two chain ring bike and it is light, light light. I was able to do the ride on that bike, but there were times when I wished for more gears. The double is fine for 1-2 days, but for more than that it would have been nice to have lower gears.