No not in 2-3 days. Yes, BIII's are known for corrosion. Mine lasted 14 seasons wet slipped in salt water. There was some evidence of corrosion on the case, but blowing the gears in the lower unit is what caused it's ultimate demise, not corrosion.
If you're going to wet slip the boat, then you absolutely should paint the bottom. I would suggest if you're going to paint the bottom, to make sure to sand it well and properly, remove all dust as described in instructions. Take the extra step to apply a barrier coat using the recommendation of the paint manufacturer. Make sure to apply the barrier coat and bottom paint according to instructions (including number of coats).
You'll also want to make sure you have zincs installed on tabs and drive and kep up on them. Paint hte drive with an aLuminum anti-fouling paint as well. Your boat shoudl already have a bonding system that should also take care of galvanic corrosion.
If you're just talking about wet slipping for a coupld of days, then you still want to make sure you kep up on your zincs no matter what, however painting is unecessary. When you do haul the boat, just make sure to clean the hull and drive and flush the outdrive and engine with fresh water using a muffs and a hose. Hook a hose up to the muffs, muffs up to the outdrive, turn on the water and fire up the engine and let it idle for about 5 min. past when it reaches operating temps. Don't leave the water running through the muffs and drive for too long with the motor turned off.