Quick answer is no. I don't think any component allows itself to be installed more than once, or appear more than once on a page like a module.
Long answer is, it could be possible with some fancy coding.
1. You could do a global search and replace on an unzipped copy of NB and change every instances of com_ninjaboard with com_theotherboard and then zip it up and install it again, as it would become basically a different component then.
2. You could make "pretend" forums, by visiting a category page, which shows only that category, copying the url and then using that url to make a menu item. But if the user clicks the "forum index" link, they will see everything again. Luckily category links are in the breadcrumbs now (soon..) ;) so they can go back to the category page too if they like.
3. There is a module that can be used to load components inside itself, mimicking the ability to load multiple components on the same page.
4. You or your client could sponsor us putting some sort of functionality to do what you want into NB. This feature isn't really a priority, so I can't see it being done in the near, or even mid term future, but $ talks and can get you any feature you like.