With a dead internal battery (which is what I suppose you meant, and not 'eternal'), I don't think you'd be able to save the game at all. The internal battery keeps track of time based events, such as the day of the week, and once it has run dry, time based events will no longer occur. Berries will not grow, and, in the case of Pokemon Ruby, the Roaming Island won't appear. If the battery has died entirely, the game will cease to save.
Assuming your internal battery has run dry and has not, in fact, bitten the dust, no, you still cannot capture Latios. It has nothing to do with your battery, however. According to Bulbapedia, http://bulbapedia.bulbagarden.net/wiki/Southern_Island, you'd need to either mix records with someone who has used an E-Reader and scanned the physical Eon Ticket into the game, or actually scan the card yourself. E-Readers haven't been available for years. And finding the actual ticket would probably be more trouble than it's worth, if you could find the E-Reader and the ticket.
Pokemon Sapphire features a cave location called Meteor Falls where unique Pokemon may be caught. It is located west of Fallarbor Town.
Shroomish is not available to be caught in the wild in Pokemon FireRed, it must be traded from Ruby or Sapphire.
Heart Scales can sometimes be found on Luvdisc when they are caught.
There are a few Pokemon you can find in victory road that will evolve those Pokemon are: Golbat, Whismur, Loudred, Aron, Lairon.
u cant caught the regis in Pokemon pearl if you want the regis migrate it from sapphire,ruby or emerald
Seedot can't be caught in the wild in Pokemon Sapphire. You must trade it from Ruby or Emerald.
Mawille can only be caught in Pokemon Ruby unfortunately
you have to mix records
catch all the Pokemon, some Pokemon will need to be caught on Sapphire and traded.
Seedot can't be caught in Sapphire. You have to trade it over from a Ruby/Emerald game
You cannot switch a pokemon from one ball to another.
he is a realy rare Pokemon 3rd generation and can be caught at a high level.
Pokemon Sapphire features a cave location called Meteor Falls where unique Pokemon may be caught. It is located west of Fallarbor Town.
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Houndour can be obtained by trading from Pokemon X or Y. It cannot be caught in the wild in Pokemon Omega Ruby and Alpha Sapphire.
Regice can not be caught in HeartGold or SoulSilver. It can however be caught in Platinum, Ruby/Sapphire, and Emerald.
Shroomish is not available to be caught in the wild in Pokemon FireRed, it must be traded from Ruby or Sapphire.