It is possible to obtain HA fossil Pokémon in OR/AS, but not from a normal fossil. The only way to obtain fossil Pokémon with their hidden abilities is to transfer it from BW or BW2 to the Pokébank, and then onto your ORAS game. So far only Amoura and Tryrunt cannot be obtained with their HA without hacking.
Source: http://pokemondb.net/pokebase/222965/how-do-you-get-fossil-pokemon-with-hidden-abilitys?show=222965#q222965
