I doubt that a little water getting into the combustion-air plumbing of the furnace is a big deal, it likely gets condensation in there regularly when a cool night leads into a warm day, for example.
As to the battery drain even when the switch is in the "Store" condition, the LP detector always gets power and will eventually drain the battery. You can take the cable off the negative post of a battery (or install a physical disconnect switch near there) to really disconnect the batteries.
Il Carriaggio — 1975 Argosy 24 | Il Progetto — 1976 Argosy 28 Center Bath | WBCCI# 15566
He has all of the virtues I dislike and none of the vices I admire. — Sir Winston Churchill