Not a dumb question.

Assuming the duct is made from steel sheet metal sections as required, and that they are properly joined, there should be no objection to either horizontal layout to an exterior wall or vertical layout to a roof using an accessible chase where needed, or some combination of these approaches.

Cooking ventilation is a potential fire hazard, significantly minimized by using hood baffles or mesh filters as a fire stop, and metal ducting capable of resisting burn through given the caloric potential of the usually very modest amount of grease that typically attaches to residential ducting.

What is important, in my view, is to ensure that combustibles not be in direct contact with the ducting. Use metal hangers or standoffs, ceramic insulation, firecode sheetrock, or other means where you might imagine ducting becoming hot enough in some theoretical fire that it could ignite proximate combustibles. (In other words, don't use crumpled newspapers for stuffing.)

Leaving the ducting exposed across the garage will enable easier access, and may reveal any unexpected grease build-up by drips from the joints. (Note that commercial ducting has to use welded joints with access ports and routine cleaning requirements, so drips outside the ducting should be non-existent in their environment.)

To best minimize grease buildup in the ducts, the air velocity should be around 1000 ft/min in cold ducts, and upwards toward 2000 ft/min in warm ducts. Of course, cold ducts will warm up if the kitchen air is warm, and a 1500 ft/min nominal design should be fine. Just start the blower well before you are shedding greasy smoke from the pan.

You will find in other threads here arguments for using a hood air velocity of 90 ft/min at the entrance aperture and scaling the counterpart CFM to a nominal blower specified CFM to achieve this flow velocity. Use the actual, pressure loss derated CFM, not the specified CFM to determine a duct diameter for your hood that gets you between 1000 ft/min and 2000 ft/min in the duct.

kas