I had the exact same diagnosis of a blocked fallopian tube, which was diagnosed after my HSG was ordered by my RE. PP is correct that it is possible to get pregnant with the good tube, but do keep in mind, which tube you ovulate from is not necessarily a 50-50 thing. You could potentially be ovulating from your blocked tube several months in a row, further decreasing your chances of conceiving. However, the opposite is also a possibility.
Had I been much younger when we started trying to conceive (I was 37.5 when we got married and immediately started TTC, and saw RE a couple months after turning 38), I probably would have wanted to try on our own a little longer before pursuing fertility treatment.
That being said, my RE would have been ok with us starting out with surgery to unblock the tube (recovery can take up to a year), or IUI, but did strongly recommend IVF and it's much higher results. We opted to go straight to IVF, due to my age, and have been successful both times. I had DD last June, and am due with #2 this August.
If you have any additional questions, feel free to PM me, or page me over on PAIF.