Theoretically, yes. That's why Apple very strongly encourages the use of Two-Factor Authentication. Once that's enabled, not only does someone need to know our password, they also need to have access to an unlocked trusted device.
If your Apple ID was compromised, the person would have access to all of your data stored in iCloud including files, photos, contacts. If they logged into your Apple ID on another Apple device, they would be able to see your messages and call logs.
If you think your Apple ID has been compromised - Apple Support