The APPS FOR OFFICE MS Word addins won't be slowing your computer done too much - about once a month they will do a License check over the internet, but apart from that the only issues are around the size of templates - for example a 50MB template will run slowly with or without software,
The other reason that Word might be running slowly is if you have experienced Word crashes. When Word crashes it leaves temp files behind associated with the document that crashed, the template it was based on, and any addins that were loaded.
These temp files exist when Word is open, but when Word shuts down it removes them. When Word crashes, it doesn't removes them and it can be confused if they already exist when it starts up.
How to remove them: