Not sure about any of the technical stuff, but if the television is an old analog type, then you'll need the converter box to translate the digital channel broadcast to analog. After the switch from analog to digital broadcasts was completed, analog TVs will be incapable of receiving over-the-air broadcasts without the addition of a set-top converter box.
You would also need an antenna to get the signals in the first place (and I think it would need to be a digital antenna too, run through the converter box). So I do think you'd need both (but someone correct me if that's wrong!!)
The reason the converter box is getting hard to find is that the switch over to digital broadcasting happened back in 2009. Converter boxes were subsidized during that time, but won't be any more because everybody should either have one for their old TV already, or have gone on to purchase new TVs that work with digital broadcasting using an antenna only. Analogues are pretty much dinosaurs.
Worst case scenario, you buy the converter box and antenna try out the antenna and see if it works by itself and return the converter box if so, but I think you will need both.