i commute a few days a week (25 miles RT) on a singlespeed, it has undoubtedly improved my fitness level, i made a thread about it a few weeks back. i think they are a great training tool that keeps you honest without the ability to shift gears, fixed even more so because you cant coast.
the only issue that you may experience (i dont know how old you are or what your overall physical health is) is the knees. i find, expecially on rolling hills with the SS that the knees really take a beating having to mash up the hills. keep an eye out for achy knees while riding...