Yes the game will reroll it's shiny odds. This is the case for most, (but not all) static encounters in the series.
Because this is Gen 2, abilities do not exist yet, which means you cannot use a Pokemon that knows Damp. Imprison was also introduced in Gen 3, which means you can't use it either. Prior to Gen 3 it is impossible to make sure that a Pokemon does not use a kamikaze move.