Basically, yeah it works. One aspect that makes it easier is that the hotter something is, the more effective radiative cooling methods are. A nuclear reactor like this is designed to run in the area of 1000 F, and it turns out that you can pump liquid salt through a radiator that size, and it can take the salt from 1200F to 700F.

Your right though, convection does make radiators far more effective, air or water just work a whole lot better than relying on radiative cooling. But regardless, you can still make radiative methods work. Every satellite in orbit has to do it, the ISS has to do it (and you can see the big grey radiators on it). And every space base will probably need to do it too.