I've done it. It's not difficult, but to keep your thighs dry you need one with a low button, otherwise it will slip of your thighs. You don't really need coat guards, because you can sit on your coat. Anyway, when closed it won't blow into the spokes very easily, but the coat guards are nice when you're getting a bit hot and you want to ride with the trench coat open. But if you don't do that, a chain guard is probably more useful.
But usually when I wear I trench coat I'm in suit, which makes a mud flap a highly appreciated accessory. Most of the time I ride with an umbrella and in a jacket or < 3/4 coat, also then the mud flap is helpful because with the wind on the umbrella, one hand at the handlebar and lifting your legs off the pedals through puddles is not the way to ride very fast.