There are places in Colorado that this could theoretically be done but so many logistical hurdles make it difficult or not worth it in general in my opinion. By the time fall rolls around most rivers in the state are about at their lowest flows before winter and many become unboatable to rafts and drift boats. The few rivers I can think of that remain boatable in the fall for a craft large enough to get you, your gear, and an animal down the river either have significant whitewater hazards that require expert level boating skills, require hard to obtain boating permits, or have land on both sides of the river that are mostly private or could easily be accessed by a vehicle. So basically some rivers you could boat down but then you would get out and hunt with everybody else on atv's. There are not many wilderness river sections here like farther north, and the streams that do flow through wilderness are generally small and have dangerous rapids that people only run in whitewater kayaks earlier in the year, if at all.
Another hurdle is permitting. If you think the western hunting arena is getting difficult to draw tags, welcome to boating in the West. Same deal. Good river permits are getting damn near impossible to draw with how popular it has become. If you have a large network of boating friends that all apply every year, usually you can get an invite and jump in on their permit but again, this is usually spring/summer. Most rivers that provide good multi-day trips require an application for permits well in advance of your trip and getting these dates to line up with your hunting trip is a monumental challenge in itself since you may draw one but not the other, or the dates you want are simply not available, or the river is too low to boat by September or October.
I won't go too in depth into boating rules and regs but usually camping is highly restricted and you must use designated areas (some that also require advanced reservation and/or have max stay limits of 1 or 2 nights so using one as a long term hunting camp would be impossible) and then packing in your own toilet system - as well as packing it out - are among the many regulations.
I can think of a few rivers where this is possible in Colorado but it would be such a headache for me to make the stars align that it would detract from the hunt. I've been boating and hunting in Colorado my entire life and I just don't think these two activities mix that well here unfortunately. If you find a place do this and it works out for you, for God's sake don't post about it on the internet. Good luck!
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