Sure you can! I use spray a bit, it is OK.
On a project like this I prefer a small roller. Adding Flotrol (latex) or Penetrol (oil) helps reduce brush and roller marks.
Many are surprised to find out cars were originally painted by brush!
Coach painting is a very old fashioned method of applying paint to a surface using a brush leaving no trace of brush marks or any other imperfections. The finished surface has to look as if it was sprayed. Don't think of it as painting an outside toilet but a way of painting horse drawn carriages like the Queen's own coach that still is painted by hand, in later years motor vehicles even Rolls Royce's were all painted in this way. Also suitable for painting commercial vehicles like coaches, trucks, vans, and of course Land Rovers.