I just tried this. Only the email is displayed. No text messages.I don't think they get backed up to OneDrive, they get backed up to Oulook.com. You can go to Outlook.com and check. Steps:
- Go to Outlook.com and login
- Click the gear and choose options
- Select "Manage Categories"
- Make sure "Contacts" has "Show in folder pane" checked
- Go back to the main Outlook.com page
- Select Contacts (under the Categories heading)
- Select "Arrange by" and choose "Conversation"
Then your text messages should be displayed.