It's All Good Without the Hood... Maybe?
It can be all good, but it is up to you to make sure your filter is clean if you have an over the range microwave in your kitchen instead of a hood system. It is not only vital for safety and proper operation, but it will also go a long way in maximizing the limited functionality of odor and smoke removal when you are cooking without a hood system.
Want to know why? Usually, over the range microwaves has lower CFM's and recirculate steam and smoke back in the kitchen after passing through a charcoal filter. Though over the range microwaves do not completely remove odors and smoke from your kitchen, they will remove some of the grease and odor particles IF you are changing the filter regularly, which means at least once a year. Some models don't even require a replacement filter, you simply have to pop it out and clean it yourself, which sounds like a really exciting eat to get your weekend started.
Be sure to check with your manufacturer for the specific filter and it's model number. Or simply contact your sales representative's to help you through the process.