Here is an answer from Sharepoint Online (Office 365) support team:
I disagree with belief of the question author that:
- "If the template is created from Office 365 SharePoint Online, you should be fine and they should work"
There are a lot of scalable issues in Sharepoint and Infopath, for example, just to mention a few:
Infopath Publishing wizard does not permit relative URLs with hard-coding initial reference
And it seems is not my own imagination. See, for example, the discussion Data Connection relative to site
The situation re is even more grave with Infopath forms of type/compatibility Workflow and/or Sharepoint List Form, which schema is locked and unmodifiable at all, see for example, my answers to question:
And these are only some of the problems with migrating/deploying anything (through templates or with aother approaches) containg Infopath forms to another Sahrepoint site