Can I wire a smoke detector so that it disables my furnace if smoke is present?
Unfortunately, with a gas furnace, that's not quite enough
The bad news for your situation is that opening the 24V R wire to the thermostat may not do what you need it to do.  Your furnace, according to pages 36 and 37 of its installation manual, and like most residential gas furnaces on the market, can and will run its blower autonomously if the plenum (fan) limit switch opens up without the thermostat calling for anything.  This is a self-protection behavior designed to limit overheating damage to the furnace's heat exchanger should it fire uncommandedly; however, it would defeat the intended operation of your duct detector were you to wire it in the way you propose.  You'd need to cut either 120V or 24V power to the furnace control in order to shut down blower operation altogether.
Nests don't like getting their plugs pulled on them, anyway
Furthermore, like most smart thermostats, the Nest assumes that its R/Rc line provides a steady supply of 24V power, especially when a C wire is provided to the thermostat.  As a result, it's liable to throw error codes, lose track of time, and otherwise behave in awkward and annoying ways if you wire the duct detector to shut off the furnace control (or even just the thermostat, as you propose).
There's just not much good a duct detector can do in most places you'd want to use a residential furnace
The final rub is that a duct smoke detector is not a substitute for other forms of smoke detection, due to inherent detection delays compared to a smoke alarm or spot/area smoke detector in the room in question.  This is stated outright in NFPA 72 17.7.5.2.1:

17.7.5.2.1 Detectors that are installed in the air duct system in accordance with 17.7.5.1(2) shall not be used as a substitute for open area protection.

Instead, they're intended to be used to shut down air-handling equipment in order to keep it from actively spreading smoke.  However, this is only generally a concern for equipment that can move more than 2000cfm of air (the figure is from IMC 606.2.1), something that even the largest model in your furnace's product line has to strain mightily to achieve.
Nonetheless, if for some reason, you have a requirement to fit duct detection to this furnace, you can do it by cutting the 24VAC &quot;hot&quot; wire from the control transformer to the connector on the furnace control board and re-routing it to a NC auxiliary contact on your duct detector.  This keeps the current draw within limits of the duct detector contacts and prevents the control board from overriding the detector's decision to stop furnace operation, but does have the drawback of confusing the thermostat if the duct detector ever has to operate in anger.