Yes it is, you would be crazy to not put some sort of extraction device in.
No it wont, firstly it will be useless, older kitchens used to have this setup, everyone I have seen has grease and crap around the fan, because it's not a concentrated source of suction, it's just picking up random air here and there.
You have three options
Conventional rangehood, either freestanding or concealed and recirculate the air via carbon filters.
Conventional rangehood, either freestanding or concealed and duct it through the roof cavity to outside the roof, you cannot legally just duct it onto the roof cavity.
Proper ceiling mounted flush rangehood, these are expensive
You will need to check the cooktop specifications, some have different height requirements, one brand of induction we are doing soon, has a 700mm height requirement, others 650mm, have seen some that wanted 750mm.