I'm not sure you'll have much luck with hairgrass in your setup. I've never tried, but I know folks that have tried it in a low-light non-CO2 setup and they've not had success.
Hairgrass isn't the most low-maintenance plant out there. They need medium to high light to really be fruitful, and you have to have lighting that can deeply penetrate the water column. Additionally, it's prone to algae issues as well if you don't maintain a very well balanced nutrient environment.
Naturally, you can give it a try and see what happens, you might surprise me. If it does take hold then you're right, it propogates by runners and will, over time, cover your tank if it's happy. My personal experience with it (e. parvula specifically) was that it took it about 2-3 months before I saw any growth, but then it took off and completely covered my 125g tank very fast once it got settled in. I was running a high-light, high-tech setup though to feed it.
Just a suggestion, have you considered microsword?