In reply to chriskane:
The only time I've done this has been on routes that turned out to be not as sound as I'd expected and I've resorted to putting quick draws on the abseil rope.
So yes, it is feasible for routes that are pretty much straight line and have solid (and accessible) places to belay the rope from.
Its a bit of a pain if its at all windy (probably best to weight down the end of the rope ) and the rope does tend to get in the way of the climbing.
You will ideally need a low stretch rope. Personally I'd just use overhand knots but alpine butterflies are a nice aesthetic knot which will also do the job.