Only true if you have fenders. Otherwise, the underside of the saddle will become soaked. (That's why Brooks recommends coating the underside as well as the top of the saddle with Proofide.) For rain riding, a waterproof cover should wrap around the entire saddle. A plastic bag is fine, but it should be secured to the seatpost with a "twist-tie."

Riding on a soaked saddle will cause the leather to sag permanently and will void the warranty. I own three B-17s and I hope they last as long as I do.