Would this work? Using a digital projector to expose photographic paper and make photographic prints that way? Would this somehow be really cool since you could project onto conventional B&W papers and get the corresponding paper-characteristics? What about colormanaging colorpapers? Does one need to project in inverse RGB? Can one introduce conventional creative effects like adding a stocking to the projectorlens for softfocus burning effects? Would the result be better/worse than inkjet printing?

No - well - it would, but you are going to be disappointed. SD projectors are about 0.5 mp and even HD ones only 1.5 MP - someone clever will know exactly!