GP and 404 handling

So, looks like the current version of Wordpress has a default 404 page. Not being in the know, I tried to look up 404 handling in here and found Tom recommending using a plugin like this: https://wordpress.org/plugins/404page/

Is there a benefit to such a plugin if Wordpress already has a 404 page and I just use Beaver Themer to create a 404 template? Will this send the correct code 404 to search engines?

I guess I want to ask if I have Beaver Themer alongside GPP, should I still use this 404 plugin?

Let me add some more context. This 404 issue is for a site that is a default site for nginx. Each site will have their own 404 as defaulted by wordpress, but if a request to the server can't be completed then Nginx will choose to serve this main site's 404. Hope that made sense.