It won't do any harm, but it's not going to make the rust disappear. It might help prevent the rusted areas from rusting further, a little bit.

A little WD-40 -- or better yet some heavier-weight oil -- before the rain, might have made the difference. But WD-40 is not a rust remover. It cleans and penetrates parts, which is very handy for breaking loose parts that have seized or started to rust together.

You have to do a some work if you want to actually deal with the rust, depending on what sort of surface is rusted. Examples, How to Remove Surface Rust From Chrome or How to Remove Rust From Steel (using cola -- you can also remove rust with caustic products like CLR). If nuts and screws are too far gone to be worth bothering with, find replacements at Stoneway Hardware.

Keeping it covered with WD-40 or other grease/wax/oil protestant products will help to delay future rust, but you have to work to keep the coating on there; it washes away as time passes.

And God help you if the Mayor listens to the idiotic Seattle Times and that blowhard Cliff Mass and dumps salt all over the roads this winter. Salt will rust the living shit out of your bike, your bike rack, your bike lock, the bridges we drive over and everyone's car. Wash the salt off every day or you're doomed.

When this happened to me, I spent some quality time with the bike and steel wool cleaning the rust off the fenders. You can use the protective coating after that.

I would have suggested Armor-All instead of WD-40.

But whatever you do, DON'T SPRAY EITHER ON THE HANDLEBAR GRIPS!. My wife loves to use this on our car steeringwheel and it just about slips out of my grip when I turning!

The most important part to be concerned about is the chain. When the chain rusts the rust spreads to the cogs. Chains are cheap, but cogs and fly wheels are not. If the chain is rusting, replace her. Except if your chain is quite old. Chains and cogs tend to stretch and meld to each other. If the cogs are well worn, you will have to replace both together.
Clean her up as best as you can. Steel wool works best. Stay away from chemicals that have strong acids. Acids eat aluminum frames. Naval Jelly is great for steal cars and boats, but will destroy or weaken an aluminum bike frame.
Vaseline works as a cheap protectant for screws and such. Just don't put it any where near the drive train- not even the deraillers. Grab some chain lube (make sure it is for bikes) and lube away.

I've had good experience using 10-80 gear oil. It's thick and gives the chain and other parts a good waterrproof coating. You might try rubbing some on with a soft cloth.

WD-40 will just destroy any grease on a bike and in the ball bearings case on the axles.

Just buy a new bike...dont bother cleaning.