I just removed the air box.  Now I have wires and connectors sitting behind the battery box in the open.  Will I have electrical problem if it gets wet?

If you wanna be a little anal about it, pull your connectors apart and squirt a little no-ox or dielectric grease in there before you reconnect. That will keep the water out and keep the contacts from corroding...

I'm a telecom guy, so I'm always working with electronics and electrical connections. Every time I pull a connector apart, it gets a dose of no-ox. Doesn't matter if it's on the bike, truck, batteries, multiplexer, inverter or whatever. Call it anal, I call it insurance!