I just finished week 5 of the C25K (after MANY tries that I abandoned) and its working great for me. However, I am a SLOW runner and mostly do this on the treadmill. When I do go outside, I have a hard time staying at a consistent pace but I am working on it. I am sure I look sillly out there running slower than people walk (or so it seems). Does anyone else run at a fairly slow pace?
The short answer is absolutely yes! Don't let your speed be any kind of barrier, keep going! Running takes a long time to get used to at first. It requires you to adapt internally to new stresses so while it may not appear that you're going any faster there will be other more subtle indications that you're improving. It should become more comfortable or you may find it becomes easier to do the usual courses near home.
If you want a good example of a slow runner who's a real role model I was working at a sprint triathlon last year and some lady did the whole thing for her 80th birthday. She was determined to run the entire run course and her husband walked along beside her the entire 5k's. She never quit her running stance and was strongly cheered when she finished by everyone there. Sure she had the slowest time at the event but that was irrelevant.
Keep at it and you'll go faster eventually, but you'll never get there if you stop.