How well a conversion works will depend largely on how the original template was created.
Specifically:
- Techniques used for placement/spacing. Word and Writer handle spacing and marginalia differently. If your template uses some means for meticulous placement, page headers/footers, frames, tables, columns, perhaps even tables within table cells, the settings for placement, margins and other spacing will most likely need adjustment. For atomated page layout changes (like a special first page) Writer will create a number of paragraph and page styles to handle the transition.
- Fields for document automation. Some fields translate easily. Others behave erratically. The "easy fields" introduced with Word 2013 will mostly be discarded, I think (I have some experience with conversion of those, but not very much...).
- Other formatting (e.g. numbered/hierarchical lists, automated paragraph transitions, special content in ToC/index) may also cause the creation of styles (sometimes a maze of interconnected paragraph, character, list and page styles).
After saving as ODT/OTT, check your template. Does it behave as expected?
Look at the styles. Do the style lists for paragraph or numbering styles contain countless "Convert..." or "WW8..." styles?
Do you still have access to Word? Sometimes the result is better when you save the file from Word (which also supports ODF formats in recent versions). Try both!
Sometimes it is a better idea to create the template from scratch instead of adjusting a converted Word template. It is sometimes a lot of work, but in the end it may save labor (and sanity). If those templates are downloaded from somewhere, see that site again. They may have specific Writer templates.
Good luck!