I also say "Do It!"
I bought my first SS this summer at a garage sale. It was an older bike and it weighed about 20 lbs with its steel frame and heavier wheels. It did have the horizontal droupouts and a true SS rear wheel.
Recently, I bought an aluminum frame and built a SS using the SS kit avialable from Nashbar (and now Performance and others). I was very lucky: with a 39 chainring and 16 cog, the chain was the exact correct length and I didn't have to use the tensioner supplied with the kit. That saved 5 ounces. The bike weighs 16.5 pounds in a 60cm frame. It has front and rear brakes. It goes up the hills here in Colorado as fast as my other bikes, both wedgies and recumbents. I am really enjoying it.
If your frame has vertical droupouts, then you might have to use the tensioner. Aside from the extra weight, one advantage could be that the rear wheel will be easier to remove and replace.
I am thinking of selling the bike I just built and convert my LiteSpeed into a SS. It would be about a pound lighter. I still like having a set of brakes for the sake of safety. I tried riding with a front brake only, but didn't feel I could stop as quickly as I wanted to, especially for around town riding.
Good luck on yoor project