I'm pretty sure the relay network effectively covers the entire galaxy; it would be foolish of the reapers not to have built it that way, assuming the Catalyst wasn't lying about their goals. There should be a relay within reasonable FTL distance of pretty much any star system (of course "reasonable distance" would be different for a reaper). Still, you're right that with only 1-2% of systems explored out of the ~300 billion star systems in the galaxy, that's a whole lot of space real estate that the Citadel races haven't seen.
It doesn't cover the entire galaxy. This seems to be a common misconception, probably because star clusters included in the network can be found across the whole galaxy. Primary relays, which form the backbone of the network, are separated by an average of thousands of light years. This fact is illustrated at least twice in the series, the most notable time being that the Reapers had to cross roughly 6,000 light years to get to the nearest relay after the Alpha relay was destroyed. Another time would be the attempts to plot a course to Ilos without using the network. And the codex, as well as related media, describe the network as such too.
And, logically, this makes sense. The Milky Way galaxy has 200-400 billion stars in it. That number is unfathomable. A network that links every star system, either directly or indirectly, is unreasonable. Honestly, even the several billion stars of a relay network that covers only 1% of the galaxy seems unreasonable.
But, you raise a good point - why would the Reapers leave vast swaths of uncharted space outside of the network? Most likely, because inhabitable worlds are actually extraordinarily rare, and the network ONLY covers every star system that has the potential to form life over several billion years, and all nearby star systems containing resources, ensuring that the probability of any civilization forming outside of the network is astronomically low. This is never explained, of course, but it is a plausible hypothesis.