In Short: Absolutely.
Cockroaches can get into a room even from holes between the very building materials that make up your domicile. They may not even be obviously visible. For instance, when doing demolition or renovations, it's not uncommon IME to see them in the interior of walls, cabinets, plumbing areas, etc.
They can flatten their bodies to extremes and will navigate towards whatever food source they can find. Even sometimes in new construction in wooded areas, if there is a target for them to seek, they will find it. From the naked eye, the house looks impenetrable. New windows, doors, seals, etc.
It's worth talking to your neighbors to see if they are also having a problem. No amount of closed doors and windows will keep them out, if they're already inside the structure.