Yes, that should not be a problem. My rather elementary understanding of the GPL suggests that it allows you to use it for whatever you want to use it for, even for a site that is behind a paywall... but the source code has to remain open-sourced.
If you have no intention of forking and selling a customised version of NodeBB, then I think you're pretty much in the clear
It is a bit different from the navigation features that are on top, because it actually changes the layout of the site.
There is already pagination customization feature in the use profile. I think that is perhaps a better place for it.
Having a shortcut like that on the home page seem pretty nifty, but right now it is very hard to discover. If we group a few features in the widget on the bottom right and made it a bit more discoverable, that could also work well.
But I would recommend against putting anything like that in the nav bar on top.