Nope. Rearming has no effect on renown. Well, not directly - It
does enable you to sink a full load of torpedoes' worth of ships, thereby adding renown
A NULL patrol grid basically means, "Go wherever you like, or just head straight for home."
[However, if you get that message when you start a new patrol (And your base was
not changed when you left) then something may be out of order.]