We have recently moved to Office 365 and looking for the best way to manage contacts. Here are some observations and requirements
1) Using Admin -> User -> Contacs: This looks to create a company wide shared address book which is great but the problem is that I can't seem to edit photos for contacts here and contacts don't sync under ActiveSync on mobile devices
2) If I create a contact and then in OWA, add that to "My Contacts" then I can get them to sync with Activesync but I still can't edit their photo
3) If I don't create a Contact in admin and instead, create it under my OWA, it syncs and allows me to add a photo but then it doesn't chare the contact with the rest of the users.
You should have no issues adding pictures to contacts, but I'd recommend using the EAC (or the Azure AD blade) for this task - the O365 admin center continues to be plagues with issues. When it comes to mobiles, there is no perfect solution though, not even many "working" solutions...