No, it can’t vent under any roof. It can go straight up and out with no issues. Or straight up and angled through the attic to the back side of a roof ridge. It depends on your roofing plan. Be sure it’s at least a 8” duct.

False chimney. My first try would be the above suggestion. Some hoods are rated to push horizontally via the duct.

Writing from the POV of functional performance over aesthetics, I would not let a street view of a down-roof blower stop me from having external kitchen ventilation. Nor would I reject without some study (or more details here) exiting the kitchen under the porch roof and then rising through the porch roof. Various coverings could be considered.

In any case, we don't know the second floor plan or attic plan or roof configuration.

Using appropriate blowers and duct diameter, one can duct almost anywhere. From an annotated fan curve from Wolf, the Broan 801642 1200 CFM rated blower can move over 600 CFM through 75 equivalent feet of duct and Wolf Pro hood baffles (exact details are missing from this graph). Every case needs to be analyzed, but a solution can often be found. Generally, only "political" considerations related to who actually controls the exterior of one's dwelling restricts ducting to the exterior. Otherwise, practical and aesthetic considerations tend to be influential.

I bet your architect designed this kitchen, venting is one of the first considerations when designing a kitchen and angled walls are never a good idea. There is nothing wrong with a hood vent on the roof you will have many vents on the roof for plumbing, heating one more honestly will not matter. I never even notice mine and I have flat roofed house. It can be vented out the roof of the porch but I see no point in having to get a higher CFM hood to travel that distance. Get a pro to come and see what is possible for your situation