My daily commute is only about 6 miles, 12 if I take the long way; both routes have a lot of hills, nothing too steep but they will slow you down if your legs aren't ready. I think it's totally manageable if you have an appropriate gear ratio for the hills. I have 68 gear inches and live in Vancouver, BC if it matters. I have to point out how much my cadence have improved since I lowered to my current ratio, I can spin 110 for a long time on the flat, and much faster going down hill; however, if you don't like to spin, I don't think a fixed gear will be suitable for your commute. It's all up to you.

I think I'll be slower going up hills with a geared bike since I'm probably going to shift a lot and not concentrate on my cadence.