Mopowers' 66 Dart Build

"In lieu of rear firewall, battery may be located in a sealed .024" steel, .032" aluminum or NHRA accepted poly box. If sealed box is used in lieu of rear firewall, box may not be used to secure battery and must be vented to outside of body".
"Relocated batteries must be fastened to frame or frame structure with a min. of two 3/8" dia. bolts."
"Metal battery hold-down straps mandatory. Strapping tape prohibited."

Can't answer about the battery causing corrosion - the battery in my car has always lived in a box, be it aluminum or one of those blue plastic ones made by Moroso. If you don't want to deal with a sealed box I'd at least use a tray at a minimum.